# Calculus

calculus
find y' if x^2y^4+3y-4x^3=5 cos x-1 (2x-y^4)+(dy/dx4y^3*x^) +dy/dx+12x^2=5(-sin x-1) is this started correctly

calculus
Chocolate Box Company is going to make open-topped boxes out of 7 × 11-inch rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way? (Round your answer to one decimal place.)

Calculus
Suppose the integral from 2 to 6 of g of x, dx equals 12 and the integral from 5 to 6 of g of x, dx equals negative 3 , find the value of the integral from 2 to 5 of 3 times g of x, dx

calculus
How would you use series to evaluate the lim(x->0) of (x-arctanx)/x^3? I'm getting stuck, and the answer says it's 1/3 but I don't know how they got there.

calculus
How would you determine the power series of 1/(1-x)^3. I know that the series of 1/(1-x) is x^n, but how would you manipulate it for this scenario?

Calculus
The length l of a rectangle is decreasing at the rate of 3cm/sec, while its width w is increasing at the rate of 3cm/sec. Find the rates of change of (1.) the area, (2.) the perimeter, (3.) the length of one diagonal at the instant when l=15 and w=6.

Calculus
A point is moving along the curve xy=12. When the point is at (4,3), the x-coordinate decreases at the rate of 2cm/sec. How fast is the y-coordinate changing at that point?

Trig identies, Calculus
Use the identities cos^2 x + sin^2 x =1 and cos2x=cos^2 x -sin^2 x to show that cos^4 x -sin^4 x = cos2x Im not sure how, I can solve my problem with half angle identities but im not sure where to start with this.

Calculus
Find the derivative of the integral from x^3 to 5 of cosk/(k^2+2). My answer is ((-cos(x^3)(3x^2))/(x^6+2).

Calculus
Find the derivative of the integral from x to 6 of ln(1 + t^2). My answer is -ln(1+x^2).

Calculus II
If {an} (a sequence) is decreasing and an > 0 for all n, then {an} is convergent. True/False?

Pre Calculus 30
1.How many positive four-digit integers can be formed that are even?9x9x9x5=3645 2.Three differently colored six-sided dice are rolled. In how many different ways can the dice turn up? 6x6x6=216 3.How many positive integers five-digit integers start with the digit 1?1x9x9x9x9=...

Calculus
Evaluate the integral: the integral of the cube root of x, dx. a. (3/4)x^(4/3)+C b. (3/2)x^(2/3)+C c. 1/(3x^(2/3))+C d. None of these I got (3x^(4/3)/4)+C. I was wondering if it would be D.

Calculus
Evaluate the integral. 1/2 integral e^(t/2) (I'm not sure what the 1/2 on the left of the integral symbol means.)

Calculus
An explosion causes debris to rise vertically with an initial velocity of 160 feet per second. In how many seconds does it attain maximum height? i know i need to use the formula: y(t)=-16t^2+Vot + yo Have: vo=160 Yo= is what i am trying to find and i dont know how to solve ...

Math/Calculus
Find the equation of the tangent line to the given equation at the indicated point a) y^2=cos(5x-3y) at ((2pi+3)/5, 1) b) x^2+x^2y+4=0 at (2,-2)

Calculus
Kayla claims that she can find an approximate value for sin 1o without using a machine to do any computations. Explain or show how she can do this (Hint: if you choose to explain the process, please be very specific. If you choose to show how it is done, you can use your ...

Differential equations,Calculus
So I have the following differential equation. The general solution I have is: t=k(-1/r)+c I now need to find the particular solution when t=0 and the radius (r) = 1cm. So k is a constant which is approx 3.9 (5/4pi) So for the particular solution im really just plugging in the...

Calculus (RATE OF CHANGE)
Two cars leave a town at the same time and travel at constant speeds along straight roads that meet at an angle of 60° in the town. If one car travels twice as fast as the other and the distance between them increases at the rate of 81 mi/h, how fast is the slower car ...

Calculus (RATE OF CHANGE)
Estimate the instantaneous rate of change at the point indicated. (Round your answer to four decimal places.) y(x) = 1/ x + 2; x = 2

Calculus
What is y=-2/7x-1 in standard form?

Calculus
What is y=-18x+13 in standard form?

calculus
One litre of water at 0 degrees Celsius will have a different volume at higher temperatures. For a temperature 0 ≤ T ≤ 30 (in Celsius) this volume (in litres) is well approximated by the function V = −aT 3 + bT 2 − cT + 1 using the coefficients a = 9.8 × 10−8, b = 3...

Calculus
Integrate sqrt(16+x^2) dx

Calculus
Integrate x^2/(sqrt(x^2-25)dx

Math - Calculus
Directions (or bearings) on Earth are measured in degrees, running from zero to 360 degrees, clockwise, starting with 0 degrees being due North. So due East for example, is 90 degrees, due South 180 degrees, and Northwest is 315 degrees. You are swinging a rock clockwise (...

Math
The letters in the words ALGEBRA, GEOMETRY, and CALCULUS are represented by the sets V= {A, L, G, E, B, R}, W= {G, E, O, M, E, T, R, Y}, and X={C, A, L, U, S}, respectively. I don't understand this can someone help?

Differential equation, calculus
Hiya, Dt/dr =k/r^2 Is this directly solvable or do I need to separate variables. I've got t=-k/r+c from the former and something along the lines of r^3=kt+c from the latter. Think I'm doing it all wrong. Thanks

Pre Calculus 30
1.How many positive three-digit integers can be made from the digits {3,4,5,6,7} if digits may be repeated? 5x4x3=60 2.In how many ways can all of the letters of the word HEXAGON be arranged if the arrangement must start with a consonant and end in a vowel? 4x3x1x2x3x4x5=1440 ...

calculus
A convex lens of a focal length f can be defined by the lens equation 1/f=1/p + 1/q if an object is a distance p from the lens, then the distance q from the lens to the images. For a particular lens, f=2cm and p is increasing find 1. a general formula for the rate of change of...

calculus
The position of a particle is given by the equation of motion s(t)= 1/(1+t)where t is in sec and s in meters find the velocity.

Pre Calculus 30
I'm having a hard time understanding the fundamental counting principal and I don't even know where to start on some of the questions.Here are a few questions I'm having trouble with. 1.Andrea, Brian, Carol, David, Emmalee, Floyd, and Gloria are to stand in a line for a ...

Calculus
Please help me solve these problems. 1.Find the inverse function (f^-1) of √3x-2 2. Integration ∫ the top is x while the bottom is 1. (sin(t))/t dt

Calculus II
Find the centroid (x¯,y¯)(x¯,y¯) of the region bounded by: y=5x^2+6x y=0 x=0 x=6 I know the integral (think, at least) is from 0 to 6 and between the first and second equation given, but I missed this lecture and have no idea how to find the center of mass

Pre-Calculus
How do I solve the equation: 3 = 2.1 sin[(pi/6)t - 5pi/6] + 3.2

calculus
The voltage in a electric current is 100 volts then with Ohm's law how do you find the instantaneous rate of change of I with respect to R ta a resistance of 20 ohms if R is increasing I know how to use the instantaneous formula but what is f(a)

Calculus
Given k(p) = |p|+4, find the average value of this function on the interval from -4 to 4. I get 6.

Math - Calculus
f(x) = { x^2sin(1/x), if x =/= 0 0, if x=0} a. find lim(x->0)f(x) and show that f(x) is continuous at x=0. b, find f'(0) using the definition of the derivative at x=0: f'(x)=lim(x->0) (f(x)-f(0)/x) c. Show that lim(x->0)f'(x) does not exist. In particular, this means ...

Calculus
Find the derivative of the integral from 2 to 5x of (sqrt(1 + u^2))/u. My answer: (sqrt(1 + 25x^2)/5x) * 5﻿﻿﻿﻿

Calculus Question! ASAP!
Hello! I have this problem: x(dx)/sqrt(9-x^2) I was wondering why I can't use trig substitution and substitute sqrt(9-x^2) for sqrt(1-sec^2) and having: integral x = 3sin(theta) dx = 3cos(theta)d(theata) integral 3sin(theta)(3cos(theta))/3cos(theta) having the 3cos(theta) ...

IB Calculus
A particle moves along the x-axis so that at any time t≥0, its velocity is given by v(t)=t^2-16t+4 What is the velocity of the particle when its acceleration is zero?

Calculus
Air is being pumped into a spherical hot air balloon at a rate of 50 cm^3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 200 cm.

Pre calculus
find 2 exponential functions with asymptote of y=80 , with points (0,176) (1,169) (3,156) (5,146) (20,101) (30,90) (60,81).one should have the base of "e"

pre-Calculus
The coffee starts out at 176 degrees, and cools off like this… Min Degrees 1 169 2 162 3 156 5 146 10 125 15 111 20 101 30 90 60 81 If he measured the coffee at 2 hours and 3 hours, what temperature would it be?

Math - Calculus
The horizontal velocity is constant. (Ignore air resistance.) Recall from your study of trigonometry that if you release a rock at a speed v in a direction that makes an angle α with the horizontal, then the initial vertical velocity vv and the horizontal velocity vh are ...

Calculus
M = log(E)-11.4/1.5 How do you express E in terms of M?

Pre calculus
explain how to do these with please. I was out a couple of days so give clear instructions. 1. sin(π/2-ϴ)secϴ 2. cot(π/2-ϴ)cosϴ

Pre-Calculus
explain how to do these with please. I was out a couple of days so give clear instructions. sin(π/2-ϴ)secϴ cot(π/2-x)cosϴ

Calculus
A hang glider is standing at the top of a 3,000 foot cliff. The hang glider jumps off and begins to descend at a constant rate of 50 feet per second, how fast is the area of the triangle formed by the cliff, the hang glider, and the ground changing at the instant when the hang...

calculus
can someone also help me ndertsand this question ; y=x^3 +2x^2+3 represents the rate of an object over the interval [7, 10]. What is the average rate of the object over the time interval?

calculus
can someone help me with this problem y=x^2 -9 represents the velocity of an object over the interval [1, 5] in meters per second. What is the displacement of the object over the time interval?

Calculus
Differentiate each 1. Y= 1/x + 3/x^2 + 2/x^3 2. Y= x^5(1+ x)^5 3. Y= 4-x^2 / 2x+3 Can someone help me I'm lost

Simplify the cubed root of 432x to the 12th power

Math; Calculus
You toss a rock up vertically at an initial speed of 55 feet per second and release it at an initial height of 6 feet. The rock will remain in the air for_______ seconds. It will reach a maximum height of_______ feet after ________ seconds.

College calculus
Find the dy/dx A. y = u sqrt u + 1; u = 2x^2 - 2/3 B. x = u/ (1 + u^3); y = u^2 /(1 + u^3) Can someone help me

Calculus
A point moves along the curve y= x^3 -3x + 5 so that x= 1/2 square root t + 3 where t is the time. At what rate is y changing when t = 4? Need some help!!!

basic calculus
A page is to contain 54 square centimeters of printed material. If the margins are 1 cm at the top and bottom and 0.5 cm at the sides, find the most economical width of the page (in cm).

Calculus
Show that there are at least two values of x in the interval (−π,π) such that x=1+sin(x)

Calculus 2
I cannot figure this out for the life of me. Maybe I am overthinking it. Money is transferred into an account at the rate of R(t)=5000t(e^-0.6t) If the account pays 2% interest compounded continuously, how much will accumulate in the account over a 9-year period?

Calculus prince@18
let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that integral. I don't know how to post integral ...

Calculus
Suppose that a car dealer offers to sell you a car for \$16500 or for payments of \$275 per month for six years. To figure out what monthly interest (x) you’re actually being charged, you’d have to solve the equation:f(x)=60x(1+x)^72-(1+x)^72+1=0

calculus
a toy balloon is in the shape of a sphere. it is being inflated at the rate of 20 in^3 / min. at the moment that the sphere has volume 64 cubic inches. what is the rate of change of the radius ?

Calculus review
let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that integral. I don't know how to post integral ...

calculus
Find the points on the graph y = -x^3 + 6x^2 at which the tangent line is horizontal. I found -x^2 + 4 = 0 are the points [4,32]

Calculus unit review
I wanted to ask this 1 questions because i didn't even know where to start. For a continuous function f(x), f(1) = 11, and Integral symbol from 1 to 5 f'(x)dx=9. Find f(5).

Continuity Calculus Help
Find the value of constants c and d that make the function below continuous at x = 4. f(x) = x2 − 3x x < 4 c x = 4 d + x x > 4 c = d = 8 I got d=8, but finding c is giving me trouble.

Continuity Calculus Help
9.0/1 points | Previous Answers SSTCalc6 2.3.046.My Notes Question Part Points Submissions Used Let f(x) = 4x2 if x > 2 4x + 3 if x ≤ 2. Show that f is continuous from the left at x = 2, but not from the right. lim f(x) = n→2− f(2) = lim f(x) = n→2+

Continuity Calculus Help
The given function is defined for all x > 0 except at x = 8. Find the value that should be assigned to f(8), if any, to guarantee that f will be continuous at 8. (If an answer does not exist, enter DNE.) f(x)= Sqrt( x^2-64/x-8)

Calculus-derivatives
At what points on the graph of f(x)=6x^2+4x-9 is the slope of the tangent line -2?

physics/calculus
A stone is thrown straight up from the edge of a roof, 600 feet above the ground, at a speed of 12 feet per second. A. Remembering that the acceleration due to gravity is -32 feet per second squared, how high is the stone 6 seconds later? B. At what time does the stone hit the...

Calculus
My question is with a multi-part homework assignment that we got in class. The information given is : A factory manufactures widgets. The rate of production of widgets after t weeks is widgets/ week. The equation for this is dx/dt=30(1-(20/((t+20)^2))). The actual questions ...

Calculus :
The rate at which ice in a skating pond is melting is given by dV/ft = -4t - 2 Where V is volume of the ice in cubic inches and t is time in days after March 1st. Skaters can use the pond as long as the volume is greater than 3 cubic ft. If the ice is 5cubic ft in march 1st, ...

Calculus
Given: A rock is thrown upward from the surface of a planet at 24m/s. It reaches a maximum height of 180 meters. Question: How fast is the rock falling when it lands on the planet? I am honestly dumbfounded by this problem. I feel that I don't have enough information, I don't ...

Pre-Calculus
determine the projection of u = 1.6 vector i + 3.3 vector j in the vector v = -2.1 vector i - 0.5 vector j direction

Pre-Calculus
a jet, in calm air conditions, travel with velocity vector (389, 389). the wind velocity (in mph) at the plane's cruising altitude is given by (0, 50). how fast is the plane's true speed

Calculus
Find the magnitude and direction angle of p=42i+35j

Calculus
Find the magnitude and direction angle of p=42i+35j

Calculus
For which values of x does the curve Y= (3x^3-3x^2+1) / (2x^2-1) , have a horizontal tangent? Show steps or explain, i dont get it

Calculus
Comute f(x) of a) f(x) = sinxcosx / sinx + cosx b) f(x) = (1-x^2) / (1+x+x^2) c) f(x) = x^7 secx

Calculus
Knowing that F(-2) = -7, F'(-2)= 12, g(-2)= -3 and g'(-2)= -9, Compute: a) h'(-2) if h(x)= f(x)g(x) b) h'(-2) if h(x) = f(x) / g(x) c) h'(-2) if h(x) = g(x) / 1+(f(x))^2 Show all steps

Calculus
Let F(x) = (x+1) / (x^2-16). Use the definition of the derivative to compute f'(x) and give its domain. Show all steps.

Calculus
A population of 1200 badgers grow by 6% every 8 years. How long does it take the population of badgers to grow 2000?

calculus
Find the volume of a solid whose base is bounded by the parabola x=y^2 and the line x=9, having square cross-sections when sliced perpendicular to the x-axis.

Calculus
Write an expanded polynomial equation based on the following information. A cubic function with a zero x=3 (with multiplicity 2), a zero at x=2, and a constant term of 18.

calculus
limx--->3- 5/x-3 I think it is -inf but I don't know how to prove it

calculus
A student throws a ball upward from a height of 48ft, initially at 32ft per second. What is the maximum height of the ball?

calculus
if limit x--->0(4-g(x)/x)=1

calculus
limx--->0 3sin 3x/4x would it be 9/4

Help! Calculus
I am so confused on how to solve this problem. I have it set up with y's on one side and x's on the other but I don't know what to do from there. Question: Solve the differential equation. The initial condition is y(0) = 1. ((x^2+1)^(1/2))(dy/dx) - (x/(2y)) = 0 y > 0 My ...

calculus
limx-->3 sin 3x/4x

calculus
find the average rate of change of the function f(x)=x^3+1 over the interval [-1,1]

calculus
Argus Company makes three​ products: A,​ B, and C. Each unit of A costs​ \$4, each unit of B costs​ \$2, and each unit of C costs​ \$1 to produce. Argus must produce at least 20​ As, 30​ Bs, and 40​ Cs, and cannot produce fewer than 200 total units of​ As, Bs, ...

calculus
if limx-->0(4-g(x)/x=1find limx--->0g(x)

calculus
find the limit x-->inf (x^2+x)^1/2-(x^2-x)^1/2 so I know I multiply by the conjugate 2x/(x^2+x)^1/2+(x^2-x)^1/2 then I don't know where to finish problem

Calculus
True or False,... Im confused If the continuous function f(x) has a domain (-∞, +∞), then either lim --> ∞ exists, or limit X--> ∞ is +-∞

basic calculus
x^3+x^2y+2y^2=0

basic calculus
x^3+x^2y+2y^2

basic calculus
find a appropriate formula for the area of a narrow circular ring....wedding band made of circular wire

basic calculus
find a appropriate formula for the area of a narrow circular ring

Calculus AB
What's the lim(x-->-infinity) sqrt(x^4-1)/(x^3-1)? I've tried solving for it but I got -1/0, which would make it undefined. Is that correct?

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