# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

**calculus**

Find the particular solution that satisfies the differential equation and the initial condition. f ''(x) = x^2, f '(0) = 8, f(0) = 8 f (x) = ?

**Calculus**

A festivals being planned. The planners need to enclose to adjacent 200 M^2 areas with fencing. They have budgeted $1000 for fencing. Fencing currently cost $10/meter. The diagram of the area is as follows: 1. Write an equation representing the total length of fence, L, ...

**College Algebra/pre-calculus**

Find the domain (This in fraction form) f(x)=x+3 x^2-4 f(x)= (This is in Radical:2-5x) Any help, thank you!

**calculus**

Find the length and width of a rectangle with maximum area that has a perimeter of (7P) units. units (smaller value) units (larger value)

**calculus**

a mass m is projected vertically upward with an initial velocity u. the air resistance is given as kv^2. the mass returns to point of projection with velocity v0. prove terminal velocity is given by vT=uv0/sqrt(u^2-v0^2). Hint distances travelled upwards and downwards are same...

**Calculus**

Function is y=x2 . Take three points, x=2, x=3, x=4. Approximate this function at these three points for a deviation Δx =0.1. Which of the three points does the approximation works best? Which point does it works worst?

**Calculus**

The number of Internet host computers (computers connected directly to the Internet, for networks, bulletin boards, or online services) has been growing at the rate of f(x) = xe^(0.1x) million per year, where x is the number of years since 1990. Find the total number of ...

**calculus**

Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.) f(x) = square root of (25 − x^2) (a) [−5, 5] minimum (x, y) = (smaller x-value) (x, y) = (larger x-value) maximum (x, y) =

**calculus**

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) tan θ = −square root of 3 answer in radian and please use the k integer

**calculus**

Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = x^2/3 − 2, [−8, 8] 1) Yes, Rolle's Theorem can be applied. 2)No, because f is not continuous on the closed interval [a, b]. 3)No, because f is not ...

**calculus**

Use a graphing utility to graph the function and find the absolute extrema of the function on the given interval. (Round your answers to three decimal places. If an answer does not exist, enter DNE.) f(x) = x^4 − 2x^3 + x + 1, [−1,3] minima (x, y) = (smaller x-...

**calculus**

Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.) f(x) = square root of (25 − x^2) (a) [−5, 5] minimum (x, y) = (smaller x-value) (x, y) = (larger x-value) maximum (x, y) = (b) [−5, 0) minimum...

**calculus**

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) tan θ = −square root of 3

**Calculus**

Linear Approximation Function is y=x2 . Take three points, x=2, x=3, x=4. Approximate this function at these three points for a deviation Δx =0.1. Which of the three points does the approximation works best? Which point does it works worst?

**Maths - calculus**

equation for the hyperbola which has vertices (0;9) and asymptotes y= 18/5 x

**Calculus**

how to make (x-3)^(2n)/4^(n) converge

**Calculus**

Find the exact value of cot(arcsin(12/13)) and cos(arcsin(1.7/2)) I know that cos(arcsin(x))=sin(arccos(x))=sqrt(1-x^2). I'm having more difficulty with the first one. Please help! Thank you

**Brief Calculus**

Increasing and Decreasing Functions. Let f(x) = 4x^3 - 9x^2 -30x +6 A. Find all critical numbers of f(x) B. Give the open intervals where f (x) is increasing and decreasing and clearly label each.

**Calculus**

How do I tell the difference between a non conic function and a conic function by looking at an equation?

**College Algebra/pre-calculus**

The Pointless Pencil Company purchases a new stamping machine for the production line that cost $8000. The equipment will be replaced in 10 years at which time its salvage value is expected to be $1000. Write a linear equation giving the value, y, of the machine during the ...

**mathematics-calculus-derivatives**

. If y=cosx, find dy/d5x please show workings #thanks

**mathematics-calculus-derivatives**

. Try this. If y=cosx find dy/d5x please show workings #thanks

**Calculus**

How do you find the derivative of sqrt(x+sqrt(x+sqrt(x+.......)))?

**Calculus**

Use the function f to solve the following: a) Local minima, local maxima, and stationary points if any. Show work. b)Intervals of upward concavity and downward concavity if any. Show work. c) Inflection points if any. Show work. f(x)=2x+1/x-2 Please, don't do steps for first ...

**Calculus**

find the area between x=tan^2y and x=-tan^2y in -pi/4<y<pi/4. I'm not sure how I can change the equations back to y=f(X) to graph. But it shouldn't really matter right? Do I do horizontal or vertical slicing? I feel like I should do horizontal since that's what the ...

**Calculus**

Determine whether the hypotheses of the Intermediate-Value Theorem are satisfied. f(x)=x^1/3 , [a,b]=[-1,1] Please, explain. Thank you.

**Calculus Urgent**

graph y=cos(pi*x/2) and y=1-x^2 and use integration to find the area in between the curve. Okay, so when I graph these two I see that they like overlap during the [-1,1] x interval. But maybe there is still a small gap in between? But I'm not sure if the [-1,1] x interval is ...

**Calculus**

Let f(x) be defined by f(x) = x/(x - 4). What is the image of f?

**Calculus**

The function f(x) = x^3 + x an inverse. Compute f^-1(0) and f^-1(2). Hint: Do not try to evaluate f^-1 explicitly.

**Calculus**

An artifact was found with 63.8% of Carbon 14, how old is the mummy, assuming the half-life of Carbon 14 is 5730 years.

**calculus**

Find the absolute extrema of the function on the closed interval. y = 1 − |t − 1|, [−9, 6]

**calculus**

Find the acceleration of the specified object. (Hint: Recall that if a variable is changing at a constant rate, its acceleration is zero.) A boat is pulled into a dock by means of a winch 8 feet above the deck of the boat (see figure). The winch pulls in rope at a rate of 5 ...

**Pre Calculus**

The revenue and cost equations for a product are R=x (50-0.002x) and C= 12x+ 150000. Where R and C are measured in dollars and x represents the number of units sold. How many units must be sold to get a profit of at least 1,650,000

**Calculus**

A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from the stack. With two smokestacks d miles apart, the concentration of the combined deposits on the line joining them, at a distance x from one stack, is given ...

**Calculus**

Suppose you are in a room that is a*10 meters. You can walk normally along the "a" meter long wall at "s" meters per second and crab walk in any direction at 1 meter per second. You start at one corner of the room, walk normally along the wall of length "a" meters for some ...

**Calculus**

Suppose x; y, and z are positive numbers that sum to 10. What is the largest possible value of xy + xz + yz? (a) First, suppose that z is a fixed parameter. Then we have to find nonnegative numbers x and y (depending on the fixed value z such that x+y = 10-z), such ...

**Calculus Applied Integrals**

A cylindrical tank of 22.1m high with radius 12.2m is filled to 10m high with water. How much work must be done to pump all the water out of the tank? (density of water is 1000\ kg/m^3) I used similar triangles somewhere in my calculations to find the answer, but I'm not sure ...

**Calculus**

A fence must be built in a large field to enclose a rectangular area of 25,600m^2. One side of the area is bounded by n existing fence, so no fence is needed for that side. Materials for the fence cost $3 per meter for the two ends and $1.50 per meter for the side opposite of ...

**Calculus**

a rancher has 1200 fet of fencing to enclose two adjacent cattle pens. What dimensions should be used so that the enclosed area is maximized?

**calculus**

an air balloon is 80ft away from you with the angle of elevation of the rising balloon changing at a rate of 4 degrees per second how fast is the balloon rising when it is 6 feet off the ground.

**AP Calculus AB**

Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -1. I don't understand the washer thickness topic which is why im having trouble with this question

**AP Calculus AB**

An object has a constant acceleration of 40 ft/sec2, an initial velocity of -20 ft/sec, and an initial position of 10 ft

**Calculus**

An airplane is flying above an observer standing on the ground. At the moment it passes overhead, the observer judges by its apparent size that the airplane’s altitude is 30,000 feet. It takes 50 seconds for the plane, moving in a straight, horizontal line, to move through ...

**Calculus**

A 15.5 foot ladder leaning up against the building .the base is 8.2 feet away from the building .how far up does the ladder reach against the building.

**Calculus**

1) A telephone company has 10,000 phones in a certain city where the basic rate is $4 per month. The officials have evidence that if the charge is reduced the number of phones will increase at an estimated rate of 1,000 phones for each 25 cent reduction. What rate would yield ...

**calculus**

the vector function r(t)=< 5 sin t, 3 sec t > , represents the position of a particle at time t. find the velocity v (t) and acceleration a (t). I don't know how to solve it without the t given. Please help

**calculus**

Find the solution of the differential equation that satisfies the given initial condition. dp/dt=2 sqrt(pt), P(1)=5 my answer: P=(2/3t^(3/2)+(15sqrt(5)-10)/15)^2 how is it wrong?

**Math**

For a calculus quiz, the teacher will choose 11 questions from the 15 in a set of review exercises. How many different sets of questions could the teacher choose

**Calculus**

Gravel is being dumped from a conveyor belt at a rate of 15 ft^3/hr and its coarseness is such that is forms a pile in the shape of an inverted right cone whose height is three times its base radius. How fast is the height of the pile increasing when the pile has a height of ...

**Calculus**

Gravel is being dumped from a conveyor belt at a rate of 15 ft^3/hr and its courseness is such that is forms a pile in the shape of an inverted right cone whose height is three times its base radius. How fast is the height of the pile increasing when the pile has a height of ...

**Calculus**

Rectangular sheet of metal 750mm by 300mm - find length of the sides of the squares to give max volume to the box, and find maximum volume of the box?

**integral calculus**

find the volume of the solid generated by revolving the area by the given curves about the indicated axis of revolution y^2=4ax,x=a;about the y-axis.

**integral calculus**

find the volume of the solid generated by revolving the area by the given curves about the indicated axis of revolution y^2=4ax,x=a;about the y-axis

**Calculus (Line Integral)**

Let c be a curve w/parameterization r(t). show that the line integral of T dr equals the length of the curve where T is the unit tangent.

**AP Calculus AB**

2. For an object whose velocity in ft/sec is given by v(t) = -t^2 + 6, what is its displacement, in feet, on the interval t = 0 to t = 3 secs? 3. Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and v(0) = 3. v...

**Calculus**

A rectangle is inscribed in the interior section cut from the parabola x = 1/4 y2 by the line x=3. One side of the rectangle lies on the line. Fine the maximum area of such a rectangle.

**Calculus Related Rates**

Two sides of a triangle are 5 and 8 and the angle between them is increasing at .05 rad/sec. how fast is the distance between the tips of the sides increasing when the angle is pi/4

**Calculus Related Rates**

A balloon is 70 feet from an observer which is rising at 15 ft/sec. At 5 seconds after lift off, how fast is the angle of elevation changing?

**Calculus Related Rates**

If a spherical balloon is inflated and its volume is increasing at a rate of 6 in^3/min. What is the rate of change of the radius when the radius is 3 inches??

**Integral calculus**

find the work required to pull up the anchor if the cable weighs 20 lb/ft in water

**Integral calculus**

find the work required to pull up the anchor if the cable weighs 20 lb/ft in water

**calculus!!!! help**

integrate:cosx+2/cosx+sinx

**calculus help!!!!! plz**

integrate:cosx+2/cosx+sinx?????

**Calculus**

(b) Find a solution of the initial-value problem. (Hint: First verify that all members of the family y = 4/x + C are solutions of the given equation.) y' = −1/4y^2 y(0) = 0.25

**Calculus**

Estimate the area under the curve f(x) = x2 + 1 from x = 0 to x = 6 by using three circumscribed (over the curve) rectangles. Answer to the nearest integer.

**Calculus**

If the area under the curve of f(x) = x2 + 2 from x = 1 to x = 6 is estimated using five approximating rectangles and right endpoints, will the estimate be an underestimate or overestimate? Underestimate Overestimate The area will be exact The area cannot be estimated with ...

**Calculus**

Two cruise ships leave the same point outside St. John’s harbor at noon. Ship A travels west at 20 km/hr, while Ship B travels south at 25 km/hr. Using calculus, determine how fast they are separating from each other at 2:00 p.m.

**Calculus**

Suppose the integral from 2 to 8 of g of x, dx equals 5, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of the integral from 2 to 6 of 2 times g of x, dx . 8 MY ANSWER 12 16 4

**Calculus**

Which of the following integrals cannot be evaluated using a simple substitution? the integral of 1 divided by the quantity x squared plus 1, dx the integral of 1 divided by the quantity x squared plus 1, dx the integral of x divided by the quantity x squared plus 1, dx (MY ...

**Calculus**

If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a to b of g of x dx ~the integral from a to a of...

**Calculus**

Given that the antiderivative of f(x) = e4x is F(x) = 1/4e^4x+C, evaluate the integral from 0 to 2 of e^4x, dx. e^8 1/4(1-e^8) 1/4(e^8-1) 1/4e^8 (MY ANNSWER)

**Calculus**

Determine the interval on which f(x) = ln(x) is integrable. (0, ‡) [0, ‡) (−‡, 0) U (0, ‡)(MY ANSWER) All reals

**Calculus**

For what values of a and b is (2, 2.5) is an inflection point of the curve x^2 y + ax + by = 0 ? What additional inflection points does the curve have?

**Calculus**

Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem given below. (Round your answer to four decimal places.) y' = 1 − xy y(0) = 0 I don't even know how to start!

**calculus**

Find the radius of the base and altitude of a right circular cone of maximum volume that could be inscribed in a sphere at radius 10 meters.

**calculus**

water is pouring into a conical cistern at the rate of 8 m^3/minute. If the height of the inverted cone is 12 meters and the radius of its circular opening is 6 meters, how fast is the water level rising when the water is 4 meters depth?

**calculus**

The surface area of a sphere initially zero increases uniformly at the rate of 26 cm^2/seconds. Find the rate at which the radius is increasing at the end of 2 seconds.

**Calculus**

Use the integral identity: ∫(a-1) (1/(1+x^2))dx=∫(1-1/a) (1/(1+u^2))du for a>1 to show that: arctan(a)+arctan(1/a)=π/2

**Calculus Related Rates**

Two people leave from the same spot and walk at 4 ft/sec going north and 5 ft/sec northwest. At 30 seconds, how fast is the distance between them changing??

**Calculus Related Rates**

A balloon, 50 feet from an observer, is rising at 20 ft/sec. At 5 seconds after lift off 1. How fast is the distance between the observer and the balloon changing? 2. How fast is the angle of elevation changing? I need help on both questions. Thanks in advance smart people!!

**Calculus**

Starting with an initial guess of x=2, use Newton’s method to approximate (Third root of 7). Stop the iterations when your approximations converge to four decimal places of accuracy. Compare with the approximation provided by your calculator I'm so stuck

**Calculus**

Using a linear approximation or differentials, approximate:(26.98)^(3/4) thank you for your help!

**calculus**

area between the curves y^2=4x , 7y=2x+20 , 2x+3y=0

**Calculus**

Find the equation of the line tangent to the curve y=(x^2+3)^1/2 that is perpendicular to the line 2x-y+7=0

**calculus**

The region bounded by y=x^2 and y=4 is rotated about the line y=-1. Find the volume.

**Calculus**

The temperature of a pan of hot water varies according to Newton's Law of Cooling: dT/dt=-k(T-A), where T is the water temperature, A is the room temperature, and k is a positive constant. If the water cools from 90°C to 85°C in 1 minute at a room temperature of 30°C, how ...

**Calculus**

Find the specific solution of the differential equation dy/dx = 4y/x^2 with condition y(−4) = e. y= -1 - 4/x <- my answer y=-1*e^(1/x) y=e^(-4/x) None of these

**Calculus**

Hi it's me again I need help with this too and I promise to never use this site again! I feel so ashamed for asking :( Use the Fundamental Theorem to evaluate the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.The answer has to have the antiderivative too. ...

**Calculus**

Can someone help and express the given integral as the limit of a Riemann sum but do not evaluate: the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.

**Calculus**

Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval and please explain, using a graph of f(x), what the Riemann sum represents. My cousin needs help with her ...

**Calculus**

Which of the following is the general solution of the differential equation dy/dx = 2x/y? y2 = x2 + C y2 = 2x2 + C <- my answer y2 = 4x2 + C x2 − y2 = C

**Calculus**

The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? x2 − y2 = 15 x2 + y2 = 15 x + y = 15 <- my answer xy = 15

**Calculus**

The temperature of a pan of hot water varies according to Newton's Law of Cooling: dT/dt=-k(T-A), where T is the water temperature, A is the room temperature, and k is a positive constant. If the water cools from 90°C to 85°C in 1 minute at a room temperature of 30°C, how ...

**Calculus**

Find the specific solution of the differential equation dy/dx = 4y/x^2 with condition y(−4) = e. y equals negative 1 minus 4 divided by x <- my answer y equals negative 1 times e raised to the 1 over x power y equals e raised to the negative 4 over x power None of these

**calculus**

Find the point on the line –3x+4y–5=0 which is closest to the point (0–5)

**Calculus**

The particular solution of the differential equation dy/dt=2*y for which y(0) = 60 is y = 60e2t y = 60 e0.5t y = 59 + et y = 30et

**Calculus**

The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? x2 − y2 = 15 x2 + y2 = 15 x + y = 15 xy = 15

**Calculus**

The temperature of a pan of hot water varies according to Newton's Law of Cooling: dT/dt=-k(T-A), where T is the water temperature, A is the room temperature, and k is a positive constant. If the water cools from 90°C to 85°C in 1 minute at a room temperature of 30°C, how ...

**Calculus**

Find the specific solution of the differential equation dy/dx = 4y/x^2 with condition y(−4) = e. y equals negative 1 minus 4 divided by x y equals negative 1 times e raised to the 1 over x power y equals e raised to the negative 4 over x power None of these

**Calculus**

Express the given integral as the limit of a Riemann sum but do not evaluate: the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.