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September 20, 2014

September 20, 2014

**Recent Homework Questions About Calculus**

Post a New Question | Current Questions

**Calculus-Applied Optimization Problem: **

Find the point on the line 6x + 3y-3 =0 which is closest to the point (3,1). Note: Your answer should be a point in the xy-plane, and as such will be of the form (x-coordinate,y-coordinate)
*Wednesday, October 30, 2013 at 12:42pm*

**Calculus**

s=çdx/(4+5cos x). By using t-substitution, i.e. t=tan(x/2) we get cos x=(1-t^2)/(1+t^2) and dx=2dt/(1+t^2). Substituting in s and simplifying, we get s= 2çdt/4(1+t^2)+5(1-t^2)=229;çdt/(9-t^2). Using standard result çdx/(a...
*Wednesday, October 30, 2013 at 4:42am*

**Calculus**

A spotlight on the ground is shining on a wall 12m away. If a woman 2m tall walks from the spotlight toward the building at a speed of 0.6m/s, how fast is the length of her shadow on the building decreasing when she is 2m from the building?
*Wednesday, October 30, 2013 at 3:46am*

**Calculus (integrals)**

Find the integral:8x^7+6/(x^8+6x)^2 I got ln(x^8+6x)^2 but apparently that is wrong.
*Tuesday, October 29, 2013 at 10:21pm*

**calculus**

Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 3m/s, how fast is the area of the spill increasing when the radius is 15m?
*Tuesday, October 29, 2013 at 7:52pm*

**Calculus**

Consider the function f(x)=-2x^3+33x^2-108x+2. For this function, there are three important intervals: (-Inf,A], [A,B], [B,Inf) where A and B are the critical points. Find A and B and for each of the important intervals, tell whether f(x) is increasing or decreasing.
*Tuesday, October 29, 2013 at 11:47am*

**Calculus**

Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^2-63x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [-8,0] Absolute maximum = Absolute minimum = (B) Interval = [-5,4] Absolute maximum = Absolute minimum = (...
*Tuesday, October 29, 2013 at 11:41am*

**Calculus**

The function f(x)=-2x^3+30x^2-96x+8 has one local minimum & one local maximum. This function has a local minimum at x equals ______ with value __________ and a local maximum at x equals _______ with value __________ .
*Tuesday, October 29, 2013 at 11:35am*

**Calculus**

Suppose f(x)= 7-8x^2, by the Mean Value Theorem, we know there exists a c in the open interval (-2,5) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
*Tuesday, October 29, 2013 at 11:14am*

**brief calculus**

I have everything right but the last question asking how many cases per week The consumer demand equation for tissues is given by q = (97 − p)^2, where p is the price per case of tissues and q is the demand in weekly sales. (a) Determine the price elasticity of demand E ...
*Tuesday, October 29, 2013 at 1:13am*

**brief calculus**

I found that c=1 but i can't get the other two questions The velocity of a particle moving in a straight line is given by v(t) = t2 + 7. (a) Find an expression for the position s after a time t . s(t) = _____ + C (b) Given that s = 1 at time t = 0, find the constant of ...
*Monday, October 28, 2013 at 11:15pm*

**Calculus**

List the critical numbers of the following function in increasing order. Enter N in any blank that you don't need to use. f(x) = (6x+6)/(5x^2+5x+5)
*Monday, October 28, 2013 at 9:48pm*

**Calculus**

Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function. If there are multiple values, separate them with commas; enter N if there are no such values. f(x)= x^2-10x+3, [0,10]
*Monday, October 28, 2013 at 9:46pm*

**calculus**

find Arc Length of (9-x^(2/3))^(3/2) I square the second derivative and have it under the square root but then get stuck at (-9x^-1)+x^(-1/3)+1 Help?
*Monday, October 28, 2013 at 8:01pm*

**calculus**

find 3 positive real numbers whose sum is 500 and whose product is as large as possible.
*Monday, October 28, 2013 at 3:17am*

**calculus**

A trough is 6 feet long and has ends that are isosceles triangles that are 1 foot high and 3.5 feet wide. If the trough is being filled at a rate of 9 cubic feet per minute, how fast is the height of the water increaseing when the height is 5 inches?
*Monday, October 28, 2013 at 12:54am*

**calculus**

A street light is at the top of a 15.000 ft. tall pole. A man 6.300 ft tall walks away from the pole with a speed of 6.000 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 45.000 feet from the pole?
*Monday, October 28, 2013 at 12:53am*

**calculus**

A plane that is flying horizontally at an altitude of 6 kilometers and a speed of 570 kilometers per hour passes directly over a radar station. How fast is the distance between the plane and the radar station increasing when the distance between the two is 14 kilometers
*Monday, October 28, 2013 at 12:52am*

**brief calculus**

Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope 6/x
*Sunday, October 27, 2013 at 6:16pm*

**Pre-Calculus**

Transform the expression from the left to the right. Tan A+ CotA to cscAsecA
*Sunday, October 27, 2013 at 3:28pm*

**Calculus Related**

tinyurl[dot]com/osguqrd Replace [dot] with a . Please provide an answer to the question in the link above.
*Sunday, October 27, 2013 at 5:50am*

**calculus**

if a snowball melts so that its surface area decreases at a rate f 1cm^2/min, find the rate at which the diameter decrease when the diameter is 10cm?
*Friday, October 25, 2013 at 6:56pm*

**Calculus**

f(x)=x^3-(4/x) find [f^(-1)(x)]' at x=6
*Thursday, October 24, 2013 at 10:36pm*

**Calculus Homework**

Find the largest region over which the function f is increasing or decreasing, for: f(x):(x-4)/(x+8) f is increasing for x=
*Wednesday, October 23, 2013 at 7:45pm*

**Calculus-Mean Value Theorem**

Find the function G(x) whose graph passes through (pi/38,-12)and has f(x) as its derivative: G(x)= I already found which is: F(x)=76(1/-19)cos(19x)+C
*Wednesday, October 23, 2013 at 5:30pm*

**Calculus**

Romat 421 (a fictitious substance) decays by about 1.5% every day. How much of a 80 pound sample remains after 5days?
*Wednesday, October 23, 2013 at 4:15pm*

**Calculus**

The population in certain country is growing at the rate of 7 % a year . If the population in the year 1995 was 190 million, (a)determine an exponential expression representing the population as a function of the year. (b) What will the population be in 2005 ? (c) What was the...
*Wednesday, October 23, 2013 at 1:08am*

**Practice Exam Calculus**

f(x) = 6sqrt{x}- 9x n the interval [1,9]. f(c)=f(9)-f(1)/9-(1)=? Verify that the conclusion of the Mean Value Theorem holds by computing Now find,c in (1, 9) so that f'(c) equals the answer you just found. c=?
*Tuesday, October 22, 2013 at 8:58pm*

**calculus**

(A) Consider the wave equation with c=1, l=1, u(0,t)=0, and u(l,t)=0. The initial data are: f(x)=x(1-x)2, g(x)=sin2(pi x). Find the value of the solution at x=0, t=10, and at x=1/3, t=0. Find the value of the solution at x=1/2, t=2. (B) Suppose that l=2, c=1/2. Draw the domain...
*Tuesday, October 22, 2013 at 4:33pm*

**Calculus**

x=7t−t^2,y=4t^(3/2) from the point (0,0) to the point (12,32), you'd have to compute integral b to a f(t)dt where a= b= f(t) =
*Tuesday, October 22, 2013 at 2:36pm*

**Calculus**

Use continuity to evaluate. as x approaches 2, lim arctan((2x^2-8)/(3x^2-6x))
*Tuesday, October 22, 2013 at 12:45pm*

**Calculus**

Evaluate the limit. as x approaches infinity, lim sqrt(x^2+6x+3)-x
*Tuesday, October 22, 2013 at 12:43pm*

**Calculus Please Help?**

A hawk flying at 25 m/s at an altitude of 150 m accidentally drops its prey. The parabolic trajectory of the falling prey is described parametrically by x=25t,y=150−4.9t^2 until it hits the ground. The variable x represents the horizontal distance traveled by the prey ...
*Tuesday, October 22, 2013 at 12:00pm*

**Calculus**

To find the length of the curve defined by x=7t−t^2,y=4t^(3/2) from the point (0,0) to the point (12,32), you'd have to compute çb to a f(t)dt where a= b= f(t) =
*Tuesday, October 22, 2013 at 9:08am*

**Calculus**

If C(x) = 18000 + 400x − 2.2x^2 + 0.004x^3 is the cost function and p(x) = 2800 − 7x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)
*Monday, October 21, 2013 at 8:53pm*

**Calculus**

If C(x) = 18000 + 400x − 2.2x^2 + 0.004x^3 is the cost function and p(x) = 2800 − 7x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)
*Monday, October 21, 2013 at 8:52pm*

**calculus**

Let y =x arcsin x, x is an element of ]-1, 1[. Show that d^2y/dx^2 = 2-x^2/(1-x^2)^3/2
*Monday, October 21, 2013 at 8:25pm*

**Calculus**

Find the limit: as x approaches 0 lim((5/x)-(5/sin(x))
*Monday, October 21, 2013 at 3:02pm*

**Calculus**

Simplify cos(sin^(-1)x)
*Monday, October 21, 2013 at 2:54pm*

**Calculus**

Simplify sin(tan^(-1)x)
*Monday, October 21, 2013 at 2:54pm*

**Calculus**

y = tan^-1(sqrt(5x^2-1)) find dy/dx
*Monday, October 21, 2013 at 2:52pm*

**Calculus**

If f(x) = 2sin(5x)arcsin(x), find f'(x).
*Monday, October 21, 2013 at 2:37pm*

**Calculus**

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges without being infinity or negative infinity, state ...
*Sunday, October 20, 2013 at 8:58pm*

**Pre-Calculus**

Find the value of the parameter: x = 3t y = t^2 + 5 t = 2
*Sunday, October 20, 2013 at 12:33pm*

**Physics**

I have a hw problem that I know involves calculus, but I'm stumped. The number density of photons left over from the Big Bang has an energy dependence of the form n(E)=(E^2)/e^(E/T)−1, where E is the energy of the photon and T is the temperature of this relic ...
*Sunday, October 20, 2013 at 1:34am*

**Pre-Calculus**

Determine the derivative at the point (2,−43) on the curve given by f(x)=7−7x−9x^2. I know that the answer is -43, but I was wondering if it was just a coincidence that the derivative at the point (2,−43) is -43, or is there a reason why -43 is the same...
*Saturday, October 19, 2013 at 10:37pm*

**Calculus**

A cable hangs between two poles of equal height and 40 feet apart. At a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is h(x)=10+(0.4)(x^1.5). The cable weighs 18.2 pounds per ...
*Saturday, October 19, 2013 at 2:17pm*

**Pre-Calculus**

f(x)= 3+5cos pi/3 (x-7) If f(x)=4, solve for x. Find 1st 3 positive values. my answers: 2.31, 5.69, 8.31
*Friday, October 18, 2013 at 8:32pm*

**PRE CALCULUS**

find exact values for the number of radians for an arc of 4pi/3 on a unit circle is the answer 4pi/3???
*Friday, October 18, 2013 at 7:26pm*

**Pre-Calculus**

Let f(x) be the function 1/(x+9). Then the quotient [f(5+h)−f(5)]/h can be simplified to −1/(ah+b). What does a and b equal to? So I understand the overall concept, and did f(5+h) = 1/(14+h) and f(5) = 1/14. Then to subtract the two, you get the common denominator ...
*Friday, October 18, 2013 at 7:17pm*

**Calculus**

If f'(x) = 2xln(-4(x^2-2.75))+(2x^3)/(x^2-2.75) find the domain.
*Thursday, October 17, 2013 at 12:27pm*

**calculus**

lim t-> -infinity for sqrt(4t^2-5t-1)/(2t-3) I get infinity or -infinity, but the real answer is -1. How does this occur?
*Wednesday, October 16, 2013 at 11:07pm*

**Calculus Homework**

You are blowing air into a spherical balloon at a rate of 7 cubic inches per second. The goal of this problem is to answer the following question: What is the rate of change of the surface area of the balloon at time t= 1 second, given that the balloon has a radius of 3 ...
*Wednesday, October 16, 2013 at 10:49pm*

**calculus**

The question is: tan(arcsinx)= I know that inverse of sin is 1/sqrt(1-x^2) however this question still confuses me. The outcome is x/sqrt(1-x^2), how did the tan create the additional x ?
*Wednesday, October 16, 2013 at 10:08pm*

**calculus**

f(x) = ln(ln(lnx)) has the domain of (e, infinity). I am not sure how this occurs however. I know in the case of ln x, x must be greater than 0. However where does e come from. e is the base of log in the case of ln, but something is just not clicking for me.
*Wednesday, October 16, 2013 at 9:56pm*

**calculus**

The question is: tan(arcsinx)= I know that inverse of sin is 1/sqrt(1-x^2) however this question still confuses me. The outcome is x/sqrt(1-x^2), how did the tan create the additional x ?
*Wednesday, October 16, 2013 at 9:45pm*

**Calculus Practice Problems**

A filter filled with liquid is in the shape of a vertex-down cone with a height of 12 inches and a diameter of 18 inches at its open (upper) end. If the liquid drips out the bottom of the filter at the constant rate of 3 cubic inches per second, how fast is the level of the ...
*Wednesday, October 16, 2013 at 7:53pm*

**Theoretical Calculus**

I have too much swag
*Wednesday, October 16, 2013 at 6:08pm*

**Calculus Practice Problems**

A boat is pulled into a dock by a rope attached to the bow (front end) of the boat and passing through a pulley on the dock that is 4 m higher than the bow of the boat. If the rope is pulled in at a rate of 3 m/s, at what speed is the boat approaching the dock when it is 8 m ...
*Wednesday, October 16, 2013 at 5:50pm*

**Homework Help Calculus**

Find the linear approximation L(x)of the function f(x)=cos(pi/(6)x) at the point x=1 and use it to estimate the value of cos(13pi/72). Here's what I did so far: L(x)=sqrt(3)/2-1/12pi(x-1)+0((x-1)^2) How do I find cos(13pi/72)
*Wednesday, October 16, 2013 at 4:19pm*

**Homework Help Calculus**

Find the linear approximation L(x) to the function f(x)=2x^(-2) at the point, x=4 and use it to estimate the value of f(39/10). I already found L(x: L(x):(1/8)-(x-4)/16+0((x-4)^2) How do you find f(39/10)?
*Wednesday, October 16, 2013 at 4:15pm*

**calc**

The cost of producing d hundred plastic toy dinosaurs per day in a small company is C(d) = 120 + 30d + 1 8d4 dollars. This company is currently producing 500 di- nosaurs each day. Using calculus, estimate how much the company should change the production to make their daily ...
*Wednesday, October 16, 2013 at 12:15pm*

**Calculus Practice Problems**

The height of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 square cm/min. At what rate is the base of the triangle changing when the height is 7 centimeters and the area is 91 square centimeters?
*Tuesday, October 15, 2013 at 10:45pm*

**Calculus Homework**

Let A(t) be the (changing) area of a circle with radius r(t), in feet, at any time t in min. If the radius is changing at the rate of dr/dt =3ft/min, find the rate of change of the area(dA/dt) at the moment in time when r = 16 ft dA/dt=
*Tuesday, October 15, 2013 at 9:54pm*

**Calculus Homework**

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.01cm thick to a hemispherical dome with a radius of 18 meters.
*Tuesday, October 15, 2013 at 9:35pm*

**Homework Help Calculus**

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 1/100cm thick to a hemispherical dome with a radius of 18 meters. I tried it but I keep getting the wrong answer.Here's what I did below: sphere: V = ⁴/&#...
*Tuesday, October 15, 2013 at 6:06pm*

**Practice Exam Calculus **

The radius of a sphere was measured to be 20cm with a a possible error of 1/5cm 1).Use linear approximation to estimate the maximum error in the calculated surface area. Leave your answer in terms of pi. 2).Use linear approximation to estimate the maximum error in the ...
*Tuesday, October 15, 2013 at 5:58pm*

**Calculus I**

If y^3 + y^2 = 7x^2 + 224 and y(2) = 6 then y'(2)= [???]
*Tuesday, October 15, 2013 at 11:50am*

**Calculus**

I need step-by-step help for solving the lim x -> 0 for the function sin(x)/(x + tan(x)) I can do simpler ones, but this one throws me off. Thanks.
*Monday, October 14, 2013 at 11:56pm*

**Pre-Calculus**

The Hotel Ventor has 400 rooms. Currently the hotel is filled. The daily rental is $ 600 per room. For every $6 increase in rent the demand for rooms decreases by 7 rooms. Let x = the number of $ 6 increases that can be made. What should x be so as to maximize the revenue of ...
*Monday, October 14, 2013 at 11:33pm*

**Calculus**

Suppose f(x) = 3x + 4. What is f^-1(x) and what is (f^-1)'(x).
*Monday, October 14, 2013 at 6:45pm*

**Calculus**

Find the derivative of the function. g(x) = (e^x)/(3 + 3x)
*Monday, October 14, 2013 at 6:22pm*

**Pre-Calculus**

It has been found that the supply of golf clubs varies linearly with its price. When the price per item was $ 76.00 ,32 items are supplied; When the price was $ 90.25 , 70 items are supplied. What is the lowest price above which golf clubs will be supplied ? So I know the ...
*Monday, October 14, 2013 at 5:57pm*

**Calculus**

"The graph of y = g(t) is provided below. Based on the graph, where is ln(g(x)) continuous?" I did not include the graph but I would like to know in what ways does ln effect the continuity of a graph. Thanks.
*Monday, October 14, 2013 at 4:25pm*

**Calculus**

Evaluate the following limit. lim e^(tanx) as x approaches the righter limit of (pi/2)
*Monday, October 14, 2013 at 3:51pm*

**Calculus**

find dy/dx for the following function. y = ln((7x - 15)/(x(x^2 + 1)^(1/7))
*Monday, October 14, 2013 at 3:49pm*

**Calculus**

If g(x) = 3 + x + e^x, find g^-1(4).
*Monday, October 14, 2013 at 3:12pm*

**Calculus**

Find a formula for the inverse of the function. f(x) = (1 + 9x) / (8 - 4x)
*Monday, October 14, 2013 at 3:06pm*

**Calculus**

Find the derivative of the function y, below. It may be to your advantage to simplify before differentiating. y = 8x(ln(x)+ln(2))-4x+pi
*Monday, October 14, 2013 at 2:50pm*

**calculus **

relative maxima and relative minima 2x^2+ 4000/x +10
*Sunday, October 13, 2013 at 11:53pm*

**Calculus**

Find the critical numbers of the function. h(t)=t^3/4-6^1/4
*Sunday, October 13, 2013 at 11:33pm*

**Pre-Calculus**

Express tan(t) in terms of cos(t), where t is in Quadrant 3
*Sunday, October 13, 2013 at 2:22pm*

**Pre-Calculus**

Write sec in terms of sin. Theta is in the third Quadrant.
*Sunday, October 13, 2013 at 1:22pm*

**Brief Calculus**

if s''(t)=((-)1/4t^3/2) +8 Then what is s''(16)?
*Friday, October 11, 2013 at 1:33pm*

**Calculus - please help!**

How do you do this? Find the volume generated by revolving the area bounded by the ellipse(x^2)/9 + (y^2)/4 = 1 about the line x=3.
*Friday, October 11, 2013 at 12:02pm*

**Calculus**

Solve: dy = [2+(y-2x+3)^0.5]dx The answer in the book is 4(y - 2x + 3) = x^2 + C, but I don't know how to solve. I've tried solving, but this ODE is not exact, nor homogeneous and I don't think the method of integrating factors apply either. Please help. Thanks in ...
*Friday, October 11, 2013 at 5:09am*

**Brief Calculus**

The position s of a point (in feet) is given as a function of time t (in seconds). s = −10 + t − 15t2; t = 8 (a) Find the point's acceleration as a function of t. s''(t)= I know this answer, it is -30 (b) Find the point's acceleration at the ...
*Thursday, October 10, 2013 at 10:39pm*

**Calculus **

How can you tell where on a graph f is discontinuous? What are the criteria?
*Thursday, October 10, 2013 at 7:55pm*

**Calculus**

Determine if Rolle's Theorem can be applied. If it can, find all values of c such that f'(c)=0. f(x)=x^3-9x, [-3,3]
*Thursday, October 10, 2013 at 4:09pm*

**Calculus**

The radius of a circular disk is given as 24 cm with a maximal error in measurement of .2 cm. What is the percentage error?
*Thursday, October 10, 2013 at 2:04pm*

**Calculus**

The linear approximation to (1/sqrt(9-x)) at x=0. What is y?
*Thursday, October 10, 2013 at 2:02pm*

**Calculus**

A cup of hot chocolate has temperature 80 C in a room kept at 20 C.? After a half hour the hot chocolate cools to 60 C. a) what is the temperature of the hot chocolate after another half hour? b) when will the chocolate have cooled to 40 C? I think I know how to do b, I'm ...
*Thursday, October 10, 2013 at 12:49pm*

**calculus**

Find the definate integal (upper limit 1, lower limit 0) (7-4x)^2dx
*Thursday, October 10, 2013 at 10:10am*

**calculus**

Find the definate integal (upper limit 1, lower limit 0) (2x^2-4x-6)dx
*Thursday, October 10, 2013 at 10:09am*

**Calculus 1**

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.
*Thursday, October 10, 2013 at 3:45am*

**Calculus 1**

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.
*Thursday, October 10, 2013 at 3:43am*

**Calculus 1**

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.
*Thursday, October 10, 2013 at 3:42am*

**Calculus 1**

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.
*Thursday, October 10, 2013 at 3:42am*

**Calculus 1**

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.
*Thursday, October 10, 2013 at 3:41am*

**Calculus**

(cos πx + sin πy)4 = 54; Implicit Differentation
*Wednesday, October 9, 2013 at 8:45pm*

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