Find the absolute maximum for the function f(x) = ((x^3)-4x+1) / ((x^4)+(x^2)+5) (x^3) = "x" to the third

Explain to me how to find the derivative of (x^2)ln(x^2) (x^2) = "x" squared

s= t^2 -3t + 2 0 < or = to t less than equal to 2 a) find the body's displacement and average velocity for the given time interval b) Find the body's speed and acceleration at the endpoints of the interval c) When, if ever during the interval does the body change direction? Thanks so much!

is there any1 there can help me to solve this problem...PLEASE.................................its included in our exam.............................................please.... PROBLEM: Find the volume of the solid S, V(S) when R is revolved about the line x=5 using the cylindrical shell method. PLEASE NEED HELP to someone whose excellent in Math!....................

Hi, my goat recently gave birth to a male goat. I wanted to keep him as a pet, but I'm not sure when to have him castrated. I've heard that it must be done within the first week, but I've also heard that if you do it too soon they have a greater chance of getting urinary calculi. I guess it has something to do with castration and their urethra not growing as big as it should. I also already have full grown fixed male ram. Will they receive along or would it be a problem to keep them in the same stall when the buck gets older? Also, do fixed male goats stink like bucks? And can they be as aggressive as bucks? My fixed ram is an angel and I don't want there to be problems between the two of them.

Does anyone know a torrent or a file i can download for Essential Calculus Early Transcendentals solution manual, it's a blue book and believe it's 1st edition? The solution manual has a red strip over the took. Can anyone help me, pleaseeeee.

A tight rope is stretched 40 feet over the ground between the Jay and Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 60 feet over point A. a) How quick is the shadow of the tightrope walker's feet moving along the ground when she is midway between the buildings? b) How far from point A is the tightrope walker when the shadow of her feet reaches the base of the Tee building? c) How quick is the shadow of the tightrope walker's feet moving up the wall of the tee building when she is 10 feet from point B? I cannot figure this one out. please help.

1. Given that x= e^tcost and y=e^tsint dx/dt)^2 + (dy/dt)^2 = 2e^2t And show that (dy/dx) = tan.t + 1/ 1 - tan.t *For dx/dt I got e^t(cost - sint) and for dy/dt I got e^t(cost + sit) both by using the product rule but I ca'nt receive the 2e^2t :( 2. y= xe^2x find i) dy/dx and ii) d^2y/dx^2 ( futher differentiation) Find also the value of (dy/dx)^2 - e^2x(d^2y/dx^2) when x = 0. *For the second question I got dy/dx to be e^2x(2x+1) but couldn't receive the right answer at the end :( Thanks a mil :)

1. domain of f(x,y) = sqrt(xy) : i understand xy must be > 0 so x >0 and y>0 ??? 2. domain of sqrt(y-x) ln(y+x) 3. domain of arcsin(xsquared + ysquared -2) help would be very appreciated!

Hi, I have to do the following math problem and need help: ∞ Σ n=2 5/n(n+2) I need to know what this converges to. Thanks

I am trying to determine the equation of the assymptotes and the verticies for the hyperbola 4xsquared + 25ysquared = 25 but dont know how to receive in the form xsquared/a + ysquared/b = 1 please help. thanks

im going to be a junior this upcoming year and i don't know if i can handle the workload. I currently have a 4.2 with every A's and 1 B. Here is my planned schedule for junior year AP english AP history Honors Chem Trig Pre-calculus AP Biology(two periods) i want to be in forensics so i think i should take ap biology. It might be a lot though so i was thinking about taking a study hall instead of pre-cal. The problem is though that i wouldn't be able to take ap calculus senior year which is what i really want to do. So should i take ap biology? Please help.

y'=x(1-y) Initial Condition: y(-2)=0

I really want to go to a school like MIT or Harvard but I am nervous to try to apply to schools like this again since I was denied for undergraduate school. I am a freshman at a state university and would really like some advice on what I could do to make my application more appealing for graduate school in math. I have been trying to participate in undergraduate research, but I have been turned away or ignored every time. I have a 4.0 in math (3.24 overall) and am taking sophomore-level math classes as a freshman. I am in introductory courses in Differential Equations and Linear Algebra. My grades so far have been an A in Multivariable Calculus and Vector Analysis and AP credits for Single-Variable Calculus. I am really interested in Complex Analysis topics like Riemann Surfaces, Several Complex Variables, Complex Dynamics, and Residue Theory and Partial Differential Equations topics in Wave Propagation, Plasma Physics, and Quantum Mechanics. Is it still possible for me to make it into a graduate school like MIT or Harvard? I want to go to a school that is very good in the fields of complex analysis and partial differential equations, but I am also interested in almost every discipline in math. Will I still be able to take advanced courses in other areas outside of my concentration if I am able to go to one of these schools?

I had to take Statistics to transfer from my community college to the four year university from which I eventually got a bachelor's degree. I am now interested in a Masters program which requires Calculus. Before Stats, I had only taken one semester of Algebra in college. What do I have to take to receive to Calculus? I had to take Stats to transfer from my community college to a four year university. I actually skipped a semester of algebra, so I have on semester of algebra and one of Stats. I got my BA and now I am thinking about going for an MA, but I need to take calculus for at least one of the programs which I am considering applying for. What do I have to take to receive into calculus?

I've done every the work myself, I just want to check if I was doing my work correctly. Find r'( t ) at π/3 if r( t ) = < tan(t), ln(2t), 3sin²(2t) > So I found the derivative of the vector to be < sec²(π/3), 1/π/3, 12sin(2π/3)cos(2π/3) > and the values I got were < 1/3, 3/π, -3√3 > please correct me if i'm wrong.

Please solve showing each step 1. integral of (ln^(3) x )/ x dx 2. integral of arctan x dx 3.integral of cos^5 x dx

A cylindrical glass of radius r and height L is filled with water and then tilted until the water remaining in the glass exactly covers its base. a)Determine a way to "slice" the water into parallel rectangular cross-sections and then set up the integral for the volume of the water. b) Determine a way to "slice" the water into parallel cross-sections that are trapezoids and then set up the integral for the volume of the water. c) Evaluate the integral d) Find the volume using common sense. (i know how) A cylindrical glass of radius r and height L is filled with water and then tilted until the water remaining in the glass exactly covers its base. a)Determine a way to "slice" the water into parallel rectangular cross-sections and then set up the integral for the volume of the water. b) Determine a way to "slice" the water into parallel cross-sections that are trapezoids and then set up the integral for the volume of the water. c) Evaluate the integral in part (a) or (b) d) Find the volume using common sense. (i know how) please help!!

For the change of glucono lactone into gluconic acid, dy/dt= -0.6y when y is measured in grams and t is measured in hours. If there are 100 grams of glucono lactone gift when t=0, how many grams are left after the first hour?

Find the limit of < [t^(3/2)]ln(t), arctan(t), e^(-2t) > as t approaches 0 For t^(3/2)*ln(t) I used L'hopital's rule and I found the limit was 0. For the limit of arctan(t) I found the limit was 0 as well. and for the limit of e^(-2t) I found the limit was 1. So if my work is correct, is the answer < 0,1,0 > ?

I have this limit problem. I have no idea on how to solve this problem. I am just going to write the whole problem.... any help would be amazing. ... 1. For the Limit, Lim sqr (x -1 ) =2 , find S > 0 that works for E = 1 x-->5 that is, find a S > 0 such that for x 0 < l x - 5 l < S ---> l sqr( x-1 ) -2 l < 1 in the interval [ 5 , 8 ] key : S = sigma E = epsilon sqr = square root l x l = absoulte value

I am having alot of trouble finding the concavitie of this problem . I have found the relative extreme , the critical numbers but I dont know how to find the concavities. this is the function : f(x) = -2cos - cos^2x , - Pie < x < pie < stand for less than or equal to critical numbers are - pie , 0 , pie Ralative Min = ( 0 , 3 ) Reelative max = ( pie , 1 ) , ( - pie , 1 ) Can anyone help me find the concavities of this function in interval - pie < x < pie

A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 20 ft/s. At what rate is his distance from second base changing when he is halfway to first base? At what rate is his distance from third base changing at the same moment?

A rancher wants to fence in an area of square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use? sorry the area is 1,000,000

I have a test tomorrow and my professor briefly went over this topic, and I'm completely lost as what to do. I'm aware of what summation notation is,but I'm not sure where to start. Any in depth explanation would be great, thanks sick do my best to label this Find the limit: Lim n--> ∞ n ____ \ \ / (1/n) ( (j/n)^3 + 1 ) /____ j=1

Please show steps with brief description of what you did. Thanks you.

I'm struggling to understand the steps necessary to complete this problem and how to set up the equations. If someone could please explain the steps or at least point me in the right direction, I would really appreciate the assistance. --emily the functions f and g are given by f(x) = int [ sqrt(4 + t^2) dt] evaluated from 0 to 3x and g(x) = f(sinx) a) find f ' (x) and g ' (x) b) write an equation for the line tangent to the graph of y = g(x) at x = pi c) write, but do not evaluate, an integral expression that represents the maximum value of g on the interval 0 < x < pi

evaluate ∫|x^2-4x|dx from -2 to 2 please show steps..thanks in advance ! <3 !

I'm struggling to understand the steps necessary to complete this problem and how to set up the equations. I think it involves the "Substitution Rule for Definite Integrals" but I'm not sure and I don't really know how to apply it. If someone could please explain the steps or at least point me in the right direction, I would really appreciate the assistance. Calculus is most definitely not my strong point, unfortunately. thank you SO much, emily the functions f and g are given by f(x) = int [ sqrt(4 + t^2) dt] evaluated from 0 to 3x and g(x) = f(sinx) a) find f ' (x) and g ' (x) b) write an equation for the line tangent to the graph of y = g(x) at x = pi c) write, but do not evaluate, an integral expression that represents the maximum value of g on the interval 0 < x < pi

A real estate office manages 50 apartments in a downtown building. When the rent is $900 per month, every the units are occupied. For every $25 increase in rent, one unit becomes vacant. On average, every units require $75 in maintenance and repairs each month. How much rent should the real esate office charge to maximize profits?

If u answer this in detailed form I will award u 10 bonus points pllllease help me

Integral(0,3) of dx/(x*sqrt(x)) I'm a little confused at were to start with this, any explanation would be great!

Hi, MIT admissions decisions are coming up and I'm starting to receive nervous so what do you think my chances are (be as cruel as necessary)? I'm an International Applicant and my SAT grades are: Math Level 2 - 800 Physics - 800 Critical Reading - 800 Math - 800 Writing - 600 I skipped a year, learned calculus early in my life, I've been part of the Portuguese International Olympiads preparation team for the second year now and last year I ranked quite well at our National Physics Olympiads. And I swim quite regularly My midyear report grades (which range from 0 to 20) are every in the 19's except Portuguese (This term was really bad and I had a 8) and Project Area (12). My recommendation letters are very good Will this bad Portuguese term affect very much my chances of getting in? I'm sorry if the post looks like I'm bragging or something like that (I'm not) but I'm really anxious and I need some objective input (postive or negative). Thanks

The top and bottom margins of a poster are 4 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 380 square centimeters, find the dimensions of the poster with the smallest area. What's the width and height

assume radius r of a sphere is expanding at a rate of 14 in/min. volume of sphere V= 4/3pir^3 and surface area is 4pir^2. Determine the rate at which the volume is changing with respect to time when r = 8 in the answer is 3584pi in/min but why?

y' - 3yx^2 = e^(x^3) I would really appreciate it if you show the steps used to find the answer. Thanks so much!

find an equation for the tangent line **step by step** f(x) = x^2 at (2,4) f(x) = 4 - x^2 at (-1,3) **thanks in advance (=

For problems 1-2, suppose that sigma a=25 (n=1, to infinity) and {s} represents the corresponding sequence of terms. 1. What is the limit (as n goes to infinity) of s ? Explain your answer. 2. What is the limit (as n goes to infinity) of a ? Explain your answer.

I have no idea how to do this question. Any ideas? What value of n gives the largest sum for f(x) =2x^2 on the interval [-1,1]? a.) n = 4 b.) n = 10 c.) n = 20 d.) n = 30 e.) n = 50 Thanks! :)

I'm completely lost on this question. Any ideas? (Please explain your reasoning so I can understand the answer): Which of the following is true for f(x) = 4 – x^2 on the interval [0,2] with n equal sub-intervals? (A left hand sum is defined as starting the interval with the first value in the interval while the right hand sum has as its last value the final value in the interval.] a.) The left-hand sum = the right-hand sum b.) The left-hand sum > the right-hand sum c.) The left-hand sum < the right-hand sum d.) The area below the curve > the left-hand sum e.) The area below the curve < the right-hand sum Thanks! :)

I'm currently in a Masters of Public Policy program, and I'm suffering in econometrics. The professor has been little help, so I'm more or less on my possess to figure it out. Are there any books that can start me off? I only have a basic grasp of calculus(my focus has been mostly political science with a dash of microeconomics).

So I want to study Mathematics in college, but I have gaps in school...and so I forgotten some of my geometry...and in two months I start Calc. 1 (calculus with analytical geometry)...is it imperative to review the geometry before i start this course..or just make sure to review my precalculus/trig.?

I feel like my brain has gone from high-speed to dial-up with chemo, and it really worries me because I am hoping to start college in September. I've always been an excellent student and had a sharp mind, but now I feel like a moron. I'll completely forget if I just took my medicine; I sometimes have to read a passage twice to fully comprehend it; essentially everything that I learned is Calculus has now been completely forgotten (not good because I was going to take a more advanced version of this year), and even my basic math skills nice of suck now; and it takes me so much longer to finish my work. Today I couldn't concentrate at every. I don't know why I am suddenly dealing with it since I just completed my sixth cycle of ABVD chemo, but it's really freaking me out. I've been dealing with horrible insomnia, so it's the only cause I think of for this sudden reaction. I'll be going to a very rigorous college, and I'm scared now that I'll just completely bomb out and humiliate myself if I don't receive my brain back. I know everyone has different experiences, but if you had it, how long did it continue after your last treatment? How long did you have it during the actual treatment? What did you do to snap out if it?

It is impossible for me to take calculus at my school unless i take pre calculus. I want to take pre calculus during the summer so i can take the science classes i want to. Would this count against me when it comes to getting into a selective college? Will this look worse on my transcript?

I am having so much difficulty with "e" with both integrating and differentiating. i am also having trouble with u substituion in evaluating integrals (general solutions and definite). i know that you need u substitution sometimes with e problems. but any help would be much appreciated!!!!

Can anyone give me some info on what kinds of things i'd be working on or learning in the following high school classes: psychology comparative religions philosophy/creative writing lit and comp physics chemistry environmental science calculus forensics language american lit/humanities contemp world lit -and how much harder is an honors or AP class compared to a normal class? i just want to know because im confused about some of them. 10 points most helpful answer Thanks!

I go to a college preparatory school, and I want to go to MIT for undergraduate college. I had a 3.3 GPA in my freshman year, and was in Algebra I reg, Geography reg, English reg, biology reg, Spanish 1 reg, and physical education. Over the summer I did volunteer work at a camp for mentally handicapped kids in South Florida. In my sophomore year I took Latin I H, Acting I H, English 10 reg., Chemistry H, Algebra II H, and World History H. and got a weighted 4.1 (unweighted 3.7). Over the summer and during the year I worked with a mentor on a research project (he is MIT alumni and will right my letter of recommendation), I took a summer pre-calc, geometry, and online health class, and worked at the camp again. My sophomore year, I scored a 34 on the ACT and 2250 on the SATs, i got National Merit Scholarship with my PSAT scores, I took two SAT subject tests (math and science) and aced both. I worked with my mentor again and was a semifinalist in a local science fair. I helped establish a robotics club at my school, and was a part of Future Business Leaders of America club. In eleventh grade i took an independent case study program as an elective, Latin on FLV (an online class), Spanish II H, English 11 H, Chemistry AP, Physics B AP, Calculus AB, US History AP. I got a weighted GPA of 4.8, Unweighted 4.0. Over the summer i took multiple college classes in science and robotics, continued my volunteer job, and went to the MIT RSI summer program for six weeks. In 12th grade I am taking the Independent case study elective, Latin III of FLV, Spanish III H, AP English Literature, Physics C, Calculus BC, Statistics, gov/eco AP. and have a 4.9 weighted or 4.0 unweighted.

A figure shows a rectangle inscribed in a given triangle of base b and height h. Find the ratio of the area of the triangle to the area of the rectangle when the are of the rectangle is maximum. [The figure shows a triangle with a long base that is not a right triangle. The rectangle has a long side n the x axis. I don't know if this figure is to scale.] Step by step walkthrough please!

I am going to senior in high school next year. I am planning to take: 1) AP Calculus BC 2) AP Physics C 3) AP Micro-Economics 4) AP US Gov't & Politics 5) AP English Language & Composition 6) AP Computer Science 7) AP Psychology 8) College Finance

Here is a problem my Calculus teacher gave us to do for some extra credit. I attempted to set the problem up, however I'm stuck because of a lack of information. My teacher says everything is there, and it would be especially easy to approach the whole problem graphically, where you represent the whole situation as a line and the Y intercept would be the initial time. I have no idea how to solve using this approach. Any help? Tips? Here is the problem: Snow began falling during the morning of February 25, and continued steadily for the next two days. At noon a snowplow began removing snow in Brooklyn at a constant rate. The plow traveled 6 km from noon to 1 PM, but only 3 km from 1 PM to 2 PM. When did the snow start to fall? Hint: Think about approaching the problem using differential equations. Remember the rate at which the plow removes snow is constant and the rate at which the height of the snow is increasing is also constant, but the rate at which the plow is moving is not constant. It is important to note that the while the plow is plowing it is still snowing, meaning that the snow is building up and being removed at the same time. Thanks Again