# Calculus

**Calculus**

How many critical points does the function f(x) = e^x - x^3 have?

**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]

**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 ...

**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.

**Differential calculus**

Find the equation of the parabola w/ v(3,-4) and with directrix y=0.

**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...

**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

**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?

**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 ...

**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 ...

**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 ...

**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?

**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 ...

**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...

**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/...

**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..

**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?

**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.

**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 ...

**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 ...

**Calculus**

Find the point on the parabola y^2=x that is closest to the point (1,7?

**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?

**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 ...

**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)

**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

**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

**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 ...

**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 ...

**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?

**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 ...

**Pre-Calculus**

14cos+7=O

**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

**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?

**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?

**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.

**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

**Calculus**

find the angle between u=7i+2j and v=-4j

**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?

**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?

**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 ...

**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.

**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 ...

**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 ...

**Differential calculus**

Find the equation of the parabola w/ v(3,-4) and with directrix y=0.

**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 ...

**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 ...

**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.

**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?

**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.

**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 ...

**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...

**Calculus**

What is the absolute value of: 3 - 8i? A. 9 B. 64 C. √55 D. √73

**Pre-Calculus**

What is the absolute value of: 3 - 8i? A. 9 B. 64 C. √55 D. √73

**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 ________...

**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 ...

**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 ...

**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]?

**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 ...

**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)

**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

**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

**calculus**

y'? 1.y=arctan(a+x/1-ax); a is constant 2.y=e^x-e^-x/e^x+e^-x

**Pre-Calculus**

Use the following vectors to answer the question. u: <-1,7> v: <6,4> What is the projection of u onto v?

**Calculus**

Given: u <-1, 7> and v <4, -3> What is the measure of the angle between them?

**Pre-Calculus**

Given: u <-1, 7> and v <4, -3> Find: (u • v)(u + v)

**Calculus**

Two sides of a triangle are 4 inches long. What should be the angle between these sides to make the area of the triangle as large as possible?

**Calculus Reimann Sum**

Approximate ∫_-2^3(x+3)dx via the Riemann sum. Use the partition of five subintervals (of equal length), with the sample point barx_i being the right end point of the i-th interval. I attempted this problem and got -40/3, but it's not being accepted. I'm not sure what I'm ...

**Calculus**

let a_i = 2^i 20 Find Σ a_(i+1)-a_i i=1

**Calculus - Special sum formulas**

Find the formula of n Σ (j+3)(j-4) j=1 I have gotten to n(n+1)(2n+1)/6 - n(n+1)/2 - 12n How do I simplify it from there?

**Calculus - Special sum formulas**

Find a formula for Sum_{j=1}^n (j+3) (j-4) So far, I have foiled to j^2-j-12. Thus,Sum_{j=1}^n(j^2) - Sum_{j=1}^n(j) - Sum_{j=1}^n(12). From Special Sum formulas, I have gotten to n(n+1)(2n+1)/6 - n(n+1)/2 - 12n What do I do from here?

**Calculus**

A particle is moving with acceleration a(t) = 24 t + 4. Its position at time t =0 is s(0) = 15 and its velocity at time t =0 is v(0) = 11. What is its position at time t = 9?

**Calculus - Differential Equations**

Use separation of variables to find the solution to the differential equation: 4 (du/dt) = u^2, subject to the initial condition u(0)=6. So far, I have: 4 du = u^2 dt 4/u^2 du = dt -4/u = t+C I am unsure what to do from this point...

**Calculus - Falling Body Problem**

Near the surface of the earth, the acceleration of a falling body due to gravity is 32 feet per second per second, provided that air resistance is neglected. If an object is thrown upward from and initial height of 3000 feet with a velocity of 75 feet per second, find its ...

**Calculus - Differential Equations**

Use separation of variables to find the solution to the differential equation: 4 (du/dt) = u^2, subject to the initial condition u(0)=6.

**Calculus**

Find the xy-equation of the curve that passes through (-2, -2) and whose slope at any point on the curve is equal to 5 times the x-coordinate of that point

**Calculus**

An offshore oil well is 4 kilometers off the coast. The refinery is 5 kilometers down the coast (see figure). Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost?

**calculus**

Consider a window the shape of which is a rectangle of height h surmounted by a triangle having a height T that is .3 times the width w of the rectangle If the cross-sectional area is A, determine the dimensions of the window which minimize the perimeter. h = w =

**Calculus**

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 1600 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that ...

**Calculus**

Sketch the given region R and then find its area. R is the region bounded by the curve y=1/x^2 and the lines y=x and y=x/8.

**Calculus**

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 1600 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that ...

**calculus**

Cars on a certain roadway travel on a circular arc of radius r. In order not to rely on friction alone to over come the centrifugal force, the road is banked at an angle of magnitude 0 from the horizontal. The banking angle must satisfy the equation rg tan 0 = v^2 where v is...

**calculus**

A patrol car is parked 50 feet from a long warehouse The light on the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes the fol lowing angles with the line perpendicular from the light to the wall? (a)=30...

**Calculus**

If f(x) = 2xsqrt(x-6), what is the value of (f^-1)(40)?

**calculus**

A point is moving along the graph of y = x2 so that dx/dt is 2 centimeters per minute. Find dy/dt when (a)x = 0 and (b)x = 3.

**Calculus**

All edges of a cube are expanding at the rate of 3 centimeters per second. How fast is the volume chang ing when each edge is (a) 1 centimeter and (b) 10 centimeters?

**calculus**

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is approx imately three times the altitude. At what rate is the height of the pile changing when it is 15 feet high?

**Calculus**

A spherical balloon is inflated with gas at the rate of 20 cubic feet per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 1 foot and (b) 2 feet?

**Calculus**

Find the dot product of: <-1, 7> and <2, ¾>.

**Calculus**

A plane traveling 500 mph (called airspeed) in the direction 120 degrees encounters a wind of 80 mph in the direction of 45 degrees. What is the resultant direction of the plane (in degrees)?

**Calculus**

Given ||v|| = 5 theta=30 degrees, write the vector v.

**Calculus**

What is the unit vector of v: <-6, -8>?

**Calculus**

Find the particular solution that satisfies the differential equation and the initial conditions. F'(x) = 4x^2 f (-1)=3 F'(t)=10t-12t^3 f (3)=2

**Calculus**

A 5ft tall person is walking toward a light 20ft off the ground at 8 ft/sec. What is the rate of change of the length of the persons shadow when they are 15ft away from the light? What is the speed of the tip of the shadow moving?

**Calculus**

True or False If F(x) and G(x) are antiderivatives of f(x), then F(x)=G(x)+C If f'(x) = g(x) then integral g(x) dx = f(x) + C Integral f(x) * g(x)dx = integral f(x)dx * integral g(x)dx I have a feeling it's False True True

**Calculus**

Find the particular solution that satisfies the differential equation and the initial conditions. f''(x) = x^2 f'(0) = 8, f(o)=4 f'(t) 10t - 12t^3, f(3) =2

**Calculus**

Find the points on the lemniscate, given below, where the tangent is horizontal 2(x^2 + y^2)^2 = 49(x^2 − y^2)

**Calculus**

Find dy/dx at the point (-3, 1) for the equation x = y^3-9y^2+5. A. -1/17 B. -1/13 C. -1/15 D. 1/17 E. 1/15 I posted this question before with a typo, but the point still doesn't appear to be on the graph of the function.

**Calculus**

Find dy/dx at the point (-3, 1) for the equation x = y^3-9x^2+5.

**pre calculus**

A rectangular parcel of land has an area of 4,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot?

**calculus**

find the economical proportion between the radius and height of the cylindrical can to give the least dimensions of a metal that encloses vloume of 10cu.in