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Homework Help: Math: Calculus

Recent Homework Questions About Calculus

Calculus
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim (tan(7x))^x x~>0
Monday, November 21, 2016 by Po

calculus
suppose that c(x)=3x^3 - 12x^2 +9000x is the cost of manufacturing x items. find a production level that will minimize the average cost of making x items
Monday, November 21, 2016 by bob

calculus
For which of the following mixtures will Ag2SO4(s) precipitate? 150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.20 M AgNO3(aq) 150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.30 M AgNO3(aq) 150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.40 M AgNO3(aq) 150.0 mL of 0.10 M Na2SO4(aq) ...
Sunday, November 20, 2016 by chris12

Calculus
A small island is 2 km off shore in a large lake. A woman on the island can row her boat 10 km/h and can run at a speed of 20 km/h. If she rows to the closest point of the straight shore, she will land 6 km from a village on the shore. How far from the village should she land ...
Sunday, November 20, 2016 by Anonymous

Calculus
A factory is located on one bank of a straight river that is 2000 m wide. On the opposite bank but 4500 m downstream is a power station from which the factory draws its electricity. Assume that it costs $3 per meter to lay an underwater cable and $1 per meter to lay an above ...
Sunday, November 20, 2016 by Anonymous

calculus antiderivation
A car traveling 60 mi/h along a straight road decelerates at a constant rate of 11 ft/s2. (a) How long will it take until the speed is 45 mi/h? (b) How far will the car travel before coming to a stop?
Sunday, November 20, 2016 by hamza

Calculus
Given that x=cos^2t and y=ln(sint) find d^2y/dx^2 at the point t=π/4
Sunday, November 20, 2016 by Omar

Calculus
Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and four sides of the box costs $1/ft2$1/ft2; the material for the base costs $2/ft2$2/ft2. Find the dimensions of the box of greatest possible volume if ...
Saturday, November 19, 2016 by Allie

Math (Calculus) (mean value theorem emergency)
Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c in the interval (-2,4) such that the tangent ...
Saturday, November 19, 2016 by Ray

Calculus
An 18 meter ladder leaning against a building makes a 70 angle with ground. How far up the building does the ladder touch?
Saturday, November 19, 2016 by Joana

Calculus
Let F(x)=f(x^4) and G(x)=(f(x))^4. You also know that a^3=15, f(a)=2, f′(a)=4, f′(a^4)=12. Find F′(a) and G′(a). I don't even know where to begin.
Saturday, November 19, 2016 by Ana

Pre-calculus
prove the identity sin2x-sin2y/sin2x+sin2y=tan(x-y)/tan(x+y​)
Saturday, November 19, 2016 by liv

Pre-calculus
prove sin(x+y)+sin(x-y)/cos(x+y)+cos(x-y)=tanx​
Saturday, November 19, 2016 by liv

Pre-calculus
If sin2x=7/25, siny=-2/sq root of 13, cot y>0, and -pi/4<x<pi/4, find sin(2y-a)
Saturday, November 19, 2016 by Liv

Calculus
Consider the function g(x) = sinxcosx. a. Find an equation of the tangent line to the graph of g at (pi/3, sqrt3/4). b. Find the critical number(s) of g on the interval [0, 2pi]. Does the function have a relative minimum, relative maximum, or neither at each critical number. ...
Friday, November 18, 2016 by Anonymous

Calculus
Use a(t) = -32 ft/sec2 as the acceleration due to gravity. (Neglect air resistance.) A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 68 feet per second. How high will the ball go?
Friday, November 18, 2016 by Kelly

Calculus
Integral f (x) * g (x) doesn't equal Integral f (x)dx * integral g (x)dx Why?
Friday, November 18, 2016 by Ian

Calculus
I'm supposed to sketch a graph of two functions that have the same derivative of a graph. The graph having a horizontal line on (0,4)
Friday, November 18, 2016 by Ian

PRE-CALCULUS
. Sam won $150,000 in the Michigan lottery and decides to invest the money for retirement in 20 years. Find the accumulated value for Sam’s retirement for each of his options: (a) a certificate of deposit paying 5.4% compounded yearly (b) a money market certificate paying 5....
Friday, November 18, 2016 by ROSE

PRE-CALCULUS
Find the accumulated value of a $5000 investment which is invested for 8 years at an interest rate of 12% compounded: (a) annually (b) semi-annually (c) quarterly (d) monthly (e) continuou
Friday, November 18, 2016 by ROSE

Calculus
Use the second fundamental theorem of calculus to find F'(x) F(x)=The integral from 0 -> x^2 (Sin(x)^2)dx
Friday, November 18, 2016 by Erika

Pre-calculus
Prove the following identities. 1. 1+cosx/1-cosx = secx + 1/secx -1 2. (tanx + cotx)^2=sec^2x csc^2x 3. cos(x+y) cos(x-y)= cos^2x - sin^2y
Friday, November 18, 2016 by Liv

Calculus
Why are these false? If a function has derivatives from both the right and left at a point then its differentiable at that point.
Thursday, November 17, 2016 by Molly

Calculus
i need help, im not sure how to get started : 1) A piece of wire 14 m long is cut into two pieces, the length of the first piece being x m. The first piece is bent into a circle, and the other is bent into a rectangle with length twice the width. Give an expression for the ...
Thursday, November 17, 2016 by Angela

calculus
A positive multiple of 11 is good if it does not contain any even digits in its decimal representation. (a) Find the number of good integers less than 1000. (b) Determine the largest such good integer. (c) Fix b ≥ 2 an even integer. Find the number of positive integers less ...
Thursday, November 17, 2016 by help

Calculus: Centers of Mass
Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y^2 = 2x, and the line x + y = 4. I've graphed the function, and it looks like a triangle with one side curved (the parabola). I'm not quite sure how to go about the rest of the problem ...
Thursday, November 17, 2016 by Anonymous

Calculus
Approximate the area under the curve y=2/x from 1 to 2 using ten approximating rectangles of equal widths and right endpoints. Round your answer to the nearest hundredth
Thursday, November 17, 2016 by Hamad hasan

re: Differential Calculus
Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation. x^2cos^2y - siny = 0 Note: I forgot the ^2 for cos on the previous question. Sorry.
Thursday, November 17, 2016 by Billy Bob

Differential Calculus
Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation. x^2cos^y - siny = 0
Thursday, November 17, 2016 by Billy Bob

Integral Calculus
I am unable to find the formula for this given sequence: {2, -6/4, 24/16, -120/64, 720/256,...} So far, I know it's at least this: a(sub(n)) = ((-1)^(n+1))/(4^(n-1)) Basically, all I'm having trouble with is finding the pattern between the numerators. If anybody can help me ...
Thursday, November 17, 2016 by Matt

Differential calculus
Find the equation of the parabola w/ v(3,-4) and with directrix y=0.
Wednesday, November 16, 2016 by Mohammed

Calculus
Find the values of c guaranteed by the mean value theorem for integrals. f(x)= x^3 [0,3]
Wednesday, November 16, 2016 by Ian

Calculus
Find the average value of the function over [1,3] and all values of x in the interval for which the function: f(x)= 4(x^2+1)/x^2 equals its average value.
Wednesday, November 16, 2016 by Erika

Calculus
Find the value of the derivative (if it exists) of f(x) = (x+3)^(4/3) at x=-3. So I got (4*(x+3)^(1/3))/3 for the derivative and 0 for the final answer.
Wednesday, November 16, 2016 by Anonymous

Calculus
Evaluate the definite integral (low) (high) -π/6 ∫ π/6 2sec(x)tan(x) dx
Wednesday, November 16, 2016 by Eric

Calculus
How many critical points does the function f(x) = e^x - x^3 have?
Wednesday, November 16, 2016 by Anonymous

Calculus
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = 4√x [4, 9]
Tuesday, November 15, 2016 by Eric

Calculus
A rectangular swimming pool is 8 m wide and 20 m long. Its bottom is a sloping plane, the depth increasing from 1 m at the shallow end to 3 m at the deep end. Water is draining out of the pool at a rate of 1 m3/min. How fast is the surface of the water falling when the depth ...
Tuesday, November 15, 2016 by Po

College Calculus
A radioactive substance has a half-life of 27 years. Find an expression for the amount of the substance at time t if 20 grams were present initially.
Monday, November 14, 2016 by Jaken

Differential calculus
Find the equation of the parabola w/ v(3,-4) and with directrix y=0.
Monday, November 14, 2016 by Mohammed

Math checking answers (Calculus Differentials)
The radius of a spherical balloon is measured as 8 inches, with a possible error of 0.02inch. a) Use differentials to approximate the possible propagated error in computing the volume of the sphere. b) Use differentials to approximate the possible propagated error in computing...
Monday, November 14, 2016 by Ray

Calculus
show that ((x − 1)/x) <( ln x) < (x − 1) for all x>1 Hint: try to apply the Mean Value Theorem to the functions f(x) = lnx and g(x) = xlnx. I'm having trouble applying the mean value theorem
Monday, November 14, 2016 by Po

Calculus - Word Problems
Suppose a spherical snowball is melting at a constant rate of 0.20in per hour. How fast is the volume changing when the radius is 10in?
Monday, November 14, 2016 by Danny

Calculus - Optimization
The post office ships a package using large package rates if the sum of the length of the longest side and the girth (distance around the package perpendicular to its length) is greater than 84in and less than or equal to 108in. Suppose you need to ship a package that is 40in ...
Monday, November 14, 2016 by Danny

Calculus
The post office ships a package using large package rates if the sum of the length of the longest side and the girth (distance around the package perpendicular to its length) is greater than 84in and less than or equal to 108in. Suppose you need to ship a package that is 40in ...
Monday, November 14, 2016 by Danny

Pre-Calculus
The amount of force required to compress a spring is inversely proportional to the distance that it has been compressed. For one certain spring, it takes 5 pounds of force to compress it from its natural length of 18 inches down to 12 inches. How much force would be required ...
Monday, November 14, 2016 by Karen

Calculus
A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when its base is 7 feet?
Sunday, November 13, 2016 by Anonymous

Integral Calculus
For what values of p is this series convergent? (summation from n = 1 to infinity) of ((-1)^(n-1))/(n^(p + 2)) A. p >= -2 B. p =/= -2 C. p > -2 D. for all p E. p > 0 You have to use the Alternating Series Test. I've already tried E, and it was wrong. I have one more ...
Sunday, November 13, 2016 by Joeseph

help me calculus
the parametric equation of a curve are x=cos2Øand y=1+sin2Ø find dy/dx and d^2y/dx^2 at Ø=pai/6.find the relationship between x and y sir steve help see my work dx/dØ=-2sin2Ø dy/dØ=2cos2Ø dy/dx=dy/dØ*dØ/dx dy/dx=2cos2Ø*1/-2sin2Ø dy/dx=-cot2Ø d^2y/dx^2=-2cosec^2(2...
Sunday, November 13, 2016 by practising and need help

another please help me check~calculus maths
y=3e^(2x)cos(2x-3) verify that d^2y/dx^2-4dy/dx+8y=0 plz help me i tried all i could but it become too complicated for me here set u=3e^(2x) v=cos(2x-3) du/dx=6e^(2x) i used chain rule dv/dx=-2sin(2x-3) dy/dx=-3e^(2x)sin(2x-3)+cos(2x-3)6e^(2x)​ d^2y/dx^2 now i did lndy/...
Sunday, November 13, 2016 by practising and need help

Calculus
Find the derivative. y=e^8x/[e^(8x)+9] y' = The answer I have is 8e^8x/[(e^8x+9)^2] but it marked it incorrect..
Sunday, November 13, 2016 by Alyssa

Calculus
Use the function f and the given real number a to find (f^-1)'(a) f(x)=(x+9)/(x+3), x>-3, a=2 f(^-1)'(a)= ? Can someone please show me how to solve this problem?
Sunday, November 13, 2016 by Alyssa

Calculus
Use the function f and the given real number a to find (f^-1)'(a) f(x)=x^3+8x-3 a=6 (f^-1)'(6)= Thank you.
Sunday, November 13, 2016 by Alyssa

Calculus
The demand equation for a product is p=88,650/(396+3x) where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 <= x <= 50. (Round your answer to two decimal places.) Please show work because I know the ...
Sunday, November 13, 2016 by Alyssa

need help calculus plz plz-sir steve
if y=3e^(2x)cos(2x-3) verify that d^2y/dx^2-4dy/dx+8y=0 plz help me i tried all i could but it become too complicated for me here set u=3e^(2x) v=cos(2x-3) du/dx=6e^(2x) i used chain rule dv/dx=-2sin(2x-3) dy/dx=-3e^(2x)sin(2x-3)+cos(2x-3)6e^(2x)​ d^2y/dx^2 now i did ...
Sunday, November 13, 2016 by practising and need help

Calculus
Find the point on the parabola y^2=x that is closest to the point (1,7?
Sunday, November 13, 2016 by Asfand

Calculus
Find the equation of the line through the point (3, 5) that cuts off the least area from the first quadrant? y-A=B(x-C) i know its slope is -3/5 which is B. But what are the values of A and C?
Sunday, November 13, 2016 by Asfand

Calculus
A ladder a = 20 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of b = 4 feet/second. Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the ...
Saturday, November 12, 2016 by Anonymous

Calculus
Suppose that f(x+h)-f(x) =-4 h x^2 - 1 h x + 4 h^2 x + 3 h^2 -3 h^3. Find: f^1(x)
Saturday, November 12, 2016 by Amy

calculus
if y is a function of x and x=e^t/(e^t+1) show that dy/dt=x(1-x)dy/dx help me plz
Friday, November 11, 2016 by fui

calculus
Could somebody help my find the critical points for y=(x-3)(x+2)^(2/3). When I take the derivative of the function I get is x=-2,3. But when I put the original function in wolfram alpha there is minimum at x=0
Friday, November 11, 2016 by Po

Calculus
The number of people expected to have a disease in t years is given by y(t) = A.3^(t/a) (i) If now (year 2016) the number of people having the disease is 1000, find the value of A. (ii) How many people are expected to have the disease in five years? (iii) When are 100,000 ...
Friday, November 11, 2016 by Muhammad

Calculus
Two ants, red ant and black ant, creeping along lines in 3-space. At time t, red ant is at point on the line x=3-t , y-2=2t , z-2t=6 and at the same time t, black ant is at the point on the line 2x=t , y-3t=2 , z=2+t a) Find the starting distance between red and black ants ...
Friday, November 11, 2016 by Muhammad

Calculus
True/false: x^2-3 is concave up on the interval (-1,1) The second derivative of x^2-3 is just 2. How do I determine concavity of a function when I can't set it equal to 0? And then how do I answer this question when it's asking for a specific interval?
Friday, November 11, 2016 by James

Calculus
I don't understand how to get q for this problem? The next steps for the problem, you just need to plug q in, but I'm not sure what to do? Do you set revenues equal to expenses? Problem: Revenue is given by R(q) = 750q and cost is given by C(q) = 6000 + 5q2. 1) At what ...
Thursday, November 10, 2016 by Mona

Pre-Calculus
14cos+7=O
Thursday, November 10, 2016 by jay

pre-calculus
create a p(x) with the following conditions: A) Vertical asymptotes at x=5 and x=-2 B) A double root x=-3 C) A horizontal asymptote at y=3
Thursday, November 10, 2016 by Cy'Anne

Calculus
If the volume of a cube is increasing at 24 in^3/min and each edge is increasing at 2 in./min, what is the length of each side of the cube? Is this 2 in?
Thursday, November 10, 2016 by Anonymous

CALCULUS
At noon, ship A is 130 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?
Wednesday, November 9, 2016 by Gagan

Calculus AB
I'm not sure how to go about this problem: Find the equation of the line tangent to the curve x^2 + 2xy + y^3 = 4 at y=1 in the 1st quadrant.
Wednesday, November 9, 2016 by Annie

Calculus
Which of the following would be the best first step when solving the following system using the substitution method? x - y = -4 ; x + 2y = 5 a. x = -4 - y b. x = -4 + y c. 2y = 5 - x d. 2y = 5 + x
Wednesday, November 9, 2016 by Iris

Calculus
find the angle between u=7i+2j and v=-4j
Wednesday, November 9, 2016 by Sade

calculus
Tom buys a rare stamp for $500. If the annual rate of inflation is 4%, how much should he ask when he sells it in 5 years in order to break even?
Wednesday, November 9, 2016 by Anna Kirakosyan

Calculus
Given 4∫8 (4 on top, 8 on bottom) f(x)dx= 12 and 4∫8 g(x)dx= 5. Evaluate the following: 4∫8 [2f(x)-3g(x)]dx Would I just put 12 in for f(c) and 5 in for g(x) then solve?
Wednesday, November 9, 2016 by Leila

Calculus
In 1626, Peter Minuit traded trinkets worth $24 to a tribe of Native Americans for land on Manhattan Island. Assume that in 1990 the same land was worth $25.2 billion. If the sellers in this transaction had invested their $24 at 7% annual interest compounded continuously ...
Wednesday, November 9, 2016 by Anna Kirakosyan

Calculus
Let F(x)= x^2 ∫ sqrt(1+t^3)dt x Find F'(4). I applied the FTC and thought that F'(4) = f(4) which in this case would be sqrt(1+4^3), giving me an answer of sqrt(65), however this is incorrect. I'm not sure how to proceed with the question.
Tuesday, November 8, 2016 by Tim

Calculus AB
There's these two word problems I don't understand. 1. A man 6 ft tall walks at a rate of 5 ft per second toward a streetlight that is 30 feet high. The man's 3-foot-tall child follows at the same speed, but 10 feet behind the man. a) Suppose the man is 90 feet from the ...
Tuesday, November 8, 2016 by Annie

Calculus
I am trying to solve a sigma/summation notation problem: n = 99, i = 4 and each term in the sequence is determined by (1/i) - (1/(i+1)). Since n = 99, I think it's safe to assume my professor does not want me to actually go through the process of subbing in "i" 99 times to ...
Tuesday, November 8, 2016 by Tim

Differential calculus
Find the equation of the parabola w/ v(3,-4) and with directrix y=0.
Tuesday, November 8, 2016 by Mohammed

Calculus
A lighthouse is built on an exposed reef, 5 miles off-shore. The shoreline is perfectly straight, and a town is located 9 miles downshore from the point on the shoreline nearest the lighthouse. The lighthouse keeper needs to go from the lighthouse to the town to get fresh ...
Tuesday, November 8, 2016 by Caroline

Calculus
A carpenter wants to make an open-topped box out of a rectangular sheet of tin 24 inches wide and 45 inches long. The carpenter plans to cut congruent squares out of each corner of the sheet and then bend the edges of the sheet upward to form the sides of the box. If the box ...
Tuesday, November 8, 2016 by kate

Basic Calculus
a rectangular field is to be enclosed with 240 m of fence. find a mathematical model expressing the area of the field as a function of its length.
Tuesday, November 8, 2016 by Carla

calculus
Integral High value= 4 lower value=0 f(x)dx f(x) = 2, x < 2 x, x ≥ 2 It's asking me to use geometric formulas to solve this without a shape given. What am I supposed to do?
Monday, November 7, 2016 by Nelson

Calculus
Find the Riemann sum for f(x) = sin x over the interval [0, 2π], where x0 = 0, x1 = π/4, x2 = π/3, x3 = π, and x4 = 2π, and where c1 = π/6, c2 = π/3, c3 = 2π/3, and c4 = 3π/2.
Monday, November 7, 2016 by Nelson

pre-calculus
Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt . The count in the bacteria culture was 900 after 20 minutes and 1600 after 30 minutes. (a) What was the initial size of the culture? (b) Find the population after 80 minutes. (c) How many ...
Monday, November 7, 2016 by kevin

Calculus
I apologize if this question is too much to ask on this site, but I am really confused. Any help would be greatly appreciated. The famous formula shown below is called Euler’s formula, after the Swiss mathematician Leonhard Euler (1707-1783). e^(a + bi) = e^(a)(cos b + i sin...
Monday, November 7, 2016 by Sade

Calculus
What is the absolute value of: 3 - 8i? A. 9 B. 64 C. √55 D. √73
Monday, November 7, 2016 by Sade

Pre-Calculus
What is the absolute value of: 3 - 8i? A. 9 B. 64 C. √55 D. √73
Monday, November 7, 2016 by Sade

calculus
Consider the function f(x) = e^sin(cos(x)) on the interval [0, 4π] a) The critical points of f are at__________? [Hint: The range of the function cos(x) is [−1, 1]. What is the range of the function cos(cos(x))?] b) Local maxima are at ________? Local minima are at ________...
Monday, November 7, 2016 by Kevin Land

calculus
Ola, I'm not understanding this question, any assistance? Thank you very much. Find the distance of the line y = 2x + 6 from the circle x^2 + y^2 = 0.5 Find the point of the line that is closest to the circle. [Hint: a point on the line is closest to the circle if it is ...
Monday, November 7, 2016 by Kevin Land

calculus
Hello there, assistance would be terrific, thank you very much. Consider the function f(x)= x^3 + 2x^2 + bx. a) The equation of the tangent line to the graph of this function at x = 1 is given by y = ? b) The tangent line intersects the x-axis at x = ? c) For what value(s) of ...
Monday, November 7, 2016 by Kevin Land

Calculus
f'(x)=sqrt(x)*sin(x) The first derivative of the f is given above. If f(0)=0, at what value of x does the function f attain its minimum value on the closed interval [0,10]?
Monday, November 7, 2016 by Mike

Calculus
Imagine making a tent in the shape of a pyramid. Assume we want the volume to be 2.2m3 to sleep two or three people. Draw a picture identifying all appropriate variables. The floor of the tent is cheaper material than the rest: assume that the material making up the dome of ...
Sunday, November 6, 2016 by Cheyenne

Calc 1
A rectangle has one side on the x-axis, one side on the y-axis, one vertex at the orgin ans one on the curve y = e^-3x , for x>(equal) 0. find the maximum area (using calculus)
Sunday, November 6, 2016 by Melissa

Calculus
A particle moves along the x-axis and its position for time t is greater than or equal to 0, is s (t)=cos(2t)+sec(t). When t=pi, the acceleration of the particle is
Sunday, November 6, 2016 by Jessica

Calculus
A continous function y=f(x) crosses x-axis at points x=-3,0,2,5. Use mean value theorem to show that function has three critical points? I am stuck in this question kindly help
Sunday, November 6, 2016 by Asfand

calculus
y'? 1.y=arctan(a+x/1-ax); a is constant 2.y=e^x-e^-x/e^x+e^-x
Sunday, November 6, 2016 by skorge

Pre-Calculus
Use the following vectors to answer the question. u: <-1,7> v: <6,4> What is the projection of u onto v?
Saturday, November 5, 2016 by Sade

Calculus
Given: u <-1, 7> and v <4, -3> What is the measure of the angle between them?
Saturday, November 5, 2016 by Iris

Pre-Calculus
Given: u <-1, 7> and v <4, -3> Find: (u • v)(u + v)
Saturday, November 5, 2016 by Iris

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