Sunday

May 29, 2016
**Calculus - Derivative**

The curve is given by x^2+2r(sqrt(y))=xy What is dx/dy when r is constant?
*Friday, May 8, 2015 by Fred*

**Calculus**

The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency f '(x) < 0 f '(x) > 0 f "(x) < 0 f "(x) > 0
*Thursday, May 7, 2015 by Gary*

**Calculus**

The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals of (0.12,1), if any, is the graph...
*Thursday, May 7, 2015 by Sarah*

**Calculus**

Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4-x)x^-3 for x>0. A. Find the x-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative minimum, or neither ...
*Thursday, May 7, 2015 by Sarah*

**Calculus**

If f is a function such that [(f(b)-f(a))/(b-a)]=2 , then which of the following statements must be true? a.f(a) = f(b) = 2 b.The slope of the tangent line to the function at x = a is 2. c.The average rate of change of the function on the interval [a, b] is 2 d.The linear ...
*Thursday, May 7, 2015 by Gary*

**Calculus**

True or False If f is continuous at x = c, then f is differentiable at x = c.
*Thursday, May 7, 2015 by Gary*

**Calculus**

The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency f '(x) < 0 f '(x) > 0 f "(x) < 0 f "(x) > 0
*Thursday, May 7, 2015 by Gary*

**Calculus**

Find the average value of the function f(x)= 8/ (3+x)^2 on the interval [0,2]
*Thursday, May 7, 2015 by Anonymous*

**Calculus**

A cable that weighs 3 lb/ft. is used to lift a golf cart which weighs 700 lbs up to the deck of a boat which is 300 ft above a loading dock. Find the work done.
*Thursday, May 7, 2015 by Anonymous*

**Calculus**

The region bounded by y= e^x, y=0, x= -1 and x=1 is rotated about the x-axis, find the volume generated.
*Thursday, May 7, 2015 by Anonymous*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1
*Thursday, May 7, 2015 by Anonymous*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.
*Thursday, May 7, 2015 by Anonymous*

**calculus 1 (I need help)**

The portion of the ellipse x^2/9+y^2/4=1 with x greater than or equals to 0 is rotated about the y-axis to form a solid S. A hole of radius 1 is drilled through the center of S, along the y-axis. Find the exact volume of the part of S that remains. Show all steps. (Hint: use ...
*Wednesday, May 6, 2015 by linda*

**calculus**

Use table of integrals to evaluate the integral of x^4 sinxdx.
*Wednesday, May 6, 2015 by beam *

**Calculus**

Find the average value of the function f(x)= 8/ (3+x)^2 on the interval [0,2]
*Wednesday, May 6, 2015 by Joe*

**Calculus**

A cable that weighs 3 lb/ft. is used to lift a golf cart which weighs 700 lbs up to the deck of a boat which is 300 ft above a loading dock. Find the work done.
*Wednesday, May 6, 2015 by Joe*

**Calculus**

The region bounded by y= e^x, y=0, x= -1 and x=1 is rotated about the x-axis, find the volume generated.
*Wednesday, May 6, 2015 by Joe*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1
*Wednesday, May 6, 2015 by Joe*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.
*Wednesday, May 6, 2015 by Joe*

**Calculus**

Find the area of the region bounded by the curves y=x^2 - 2x and y= x + 4
*Wednesday, May 6, 2015 by Joe*

**Pre-Calculus**

Evaluate. 1-|200+||-2|(-5)^3|| I get 49 as an answer
*Wednesday, May 6, 2015 by Lucina*

**calculus**

find the exact arc length of the curve: y=0.5(e^x + e^-x) for 0 is less than or equal to x and x is less than or equals to ln2.
*Wednesday, May 6, 2015 by may*

**Calculus **

What is the derivative of tan(1-x)^(1/2)?
*Wednesday, May 6, 2015 by Lola*

**Calculus**

The graph of f '(x) is continuous and decreasing with an x-intercept at x = -3. Which of the following statements must be true?
*Monday, May 4, 2015 by joe9*

**Calculus max/min**

d=0.767. There are two parallel sidewalks that are separated by the park that is 600 feet wide. You are standing on the south sidewalk facing east. On the north sidewalk, 2000 feet ahead of you, is a bus stop. You can walk on the sidewalk at 5.5+d feet per sec. You can walk ...
*Sunday, May 3, 2015 by John*

**Calculus 2**

Find the radius of convergence and interval of convergence of the series. There is an infinity sign on top of the summation symbol and "n=1" underneath it. To the right of the summation symbol is x^n/5n! How would you find the radius of convergence and interval of ...
*Sunday, May 3, 2015 by Sena*

**Calculus**

A wedge is cut from a right circular cylinder of radius r by two planes, one perpendicular to the axis of the cylinder and the other making an angle (beta) with the first. Find the volume of the wedge by slicing perpendicular to the y-axis. Please show all steps
*Sunday, May 3, 2015 by Beam*

**calculus**

h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. What values of a make h(x) strictly decreasing? I know h'(x) has to be less than zero for h(x) to be decreasing and h'(x) = 1-asin(ax). I'm not sure where to go from here...
*Saturday, May 2, 2015 by kaitlyn*

**Optimization Calculus**

A three sided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. There is 96 ft of fencing available. Find the maximum enclosed area and the dimensions of the corresponding enclosure. I drew a picture of it and I got ...
*Saturday, May 2, 2015 by Nicole*

**Calculus**

h(x) = x+cos(ax) is a family of functions where a is a positive constant such that 0<a<4. Which values of a make h(x) strictly decreasing? Justify your answer. I can't figure this out and help would be appreciated. Thanks in advance!
*Saturday, May 2, 2015 by ashley*

**Calculus**

h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. For what values of a will h(x) have a relative maximum at x=1? So I found the derivative and got h'(x) = 1- asin(ax). Then I plugged in 1 for x and set the derivative equal to zero, so I have 1 + ...
*Friday, May 1, 2015 by ashley*

**Calculus**

h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. For what values of a will h(x) have a relative maximum at x=1? So I found the derivative and got h'(x) = 1- asin(ax). Then I plugged in 1 for x and set the derivative equal to zero, so I have 1 - ...
*Friday, May 1, 2015 by ashley*

**Calculus**

Imagine making a tent in the shape of a right prism whose cross-section is an equilateral triangle (the door is on one of the triangular ends). Assume we want the volume to be 2.2 m3, to sleep two or three people. The floor of the tent is cheaper material than the rest: assume...
*Thursday, April 30, 2015 by Lizz*

**Calculus**

What is the solution to the following system of equations -2x+3y+z=5 x+5y+2z=17 To do this, I used elementary operations and isolated x to get 13y+5z=37. Is that correct so far? How would I continue?
*Thursday, April 30, 2015 by Sara*

**Calculus**

How would I find the equilibrant of three vectors? I am given a graph of three different vectors which meet at the point (0,0)
*Thursday, April 30, 2015 by Sara*

**Calculus**

If 3(a,3,2)-2(3,b,b)=(-3,1,-2) determine a and b. Describe the set spanned by the vectors. I don't know how to answer this
*Thursday, April 30, 2015 by Sara*

**Calculus**

I'm not sure how to do this; I figured I should use separation of variables but I got the wrong equation. Help is appreciated, thanks! If dy/dx=(1+x)/(xy), x > 0, and y = –4 when x =1, when x =3, y = ? A. 6.433, −6.233 B. 3.898, −3.898 C. 4.711, −...
*Thursday, April 30, 2015 by ashley*

**Calculus**

What are the coordinates of the point on the graph of f(x)=(x+1)(x+2) at which the tangent is parallel to the line with equation 3x-y-1=0? a)(-3,2) b)(-1,0) c)(0,2) d)(1,6) To answer this, I put f(x)=(x+1)(x+2) into the form f(x)=x^2+3x+2 and found the derivative which is f&#...
*Thursday, April 30, 2015 by Sara*

**Calculus and Vectors **

A plane is flying south east at a constant speed of 900km/h. The wind is blowing towards the north at 100km/h. Determine the resultant velocity of the plane relative to the ground.
*Wednesday, April 29, 2015 by John*

**Calculus**

What does it mean to span in R2? I have this question: Which of the following sets if vectors span R2? a) {(1,1),(-2,-2)} b) {(1,1),(1,2)} c) {(1,2),(1/2,2)} d) {(-1,1),(1,-1)}
*Wednesday, April 29, 2015 by Sara*

**Calculus**

An airplane is heading due east with an airspeed of 220km/h when it encounters a wind from the south at 76km/h. What is the direction of the resultant velocity of the airplane The answer is E19.06°N but I don't know how
*Wednesday, April 29, 2015 by Sara*

**calculus**

Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y^4."
*Wednesday, April 29, 2015 by Anonymous*

**Calculus-limits**

What is the limit as x approaches a of (sinx-sin a)/(x-a)? a. -sin a b. cos a c. -sin x d. cos x e. undefined Thanks!
*Wednesday, April 29, 2015 by ashley*

**calculus**

For the function f(x)=x^3e^x, determine intervals of increase and decrease and the absolute minimum value of f(x) To do this I found the derivative which is f'(x)=3x^2e^x. Then I set it to zero: f'(x)=0 0=3x^2e^x How would I isolate x? And when I do, I would sub that x...
*Wednesday, April 29, 2015 by Sara*

**Calculus-limits**

I'm studying for the AP exam and I can't figure this problem out. I thought the answer was negative infinity but that isn't an option. Thank you in advance! What is the limit as x approaches infinity of (9x-x^2-7x^4)/(x^3+12x)? a. 9 b. 7 c. -7/12 d. -7 e. Does not ...
*Wednesday, April 29, 2015 by ashley*

**Calculus**

Can you please explain how I would solve these questions? 1) Which point is 2 units from the line 12x-9y-5=0? a)(8,3) b)(7/6, -7/3) c)(14,6) d)(1,1) 2.) Which of the following sets of vectors spans R2: a) {(1,1),(-2,-2)} b) {(1,1),(1,2)} c) {(1,2),(1/2,2)} d) {(-1,1),(1,-1)}
*Wednesday, April 29, 2015 by Sara*

**calculus**

1.Solve the differential equation dy/dx= y^2/x^3 for y=f(x) with the condition y(1) = 1. 2.Solve the differential equation y prime equals the product of 2 times x and the square root of the quantity 1 minus y squared. Explain why the initial value problem y prime equals the ...
*Tuesday, April 28, 2015 by Anonymous*

**Pre-Calculus**

Explain the difference between sin^-1(x) and 1/sin(x), Are there different expressions for both these functions?
*Tuesday, April 28, 2015 by Andrea*

**Pre-Calculus**

At 34 degrees north latitude, the longest day of the year has 14.273 hours of daylight, and the shortest day 9.726 hours. If the equinox falls on march 21(day 80), model the hours of the daylight by day?
*Tuesday, April 28, 2015 by Jessica*

**Pre-Calculus**

f(x) is a sinusoidal curve with maximum at f(0)=10 and next minimum at f(6)=0. Find the equation?
*Tuesday, April 28, 2015 by Richard*

**Calculus**

Piecewise function problem. Let f(x)={ax^2+1/3, x is greater than or equal to 1; bx-10/3, x<1. If the function is differentiable, find the sum of a+b.
*Tuesday, April 28, 2015 by Anonymous*

**Calculus**

The rate of change of atmospheric pressure P with respect to the altitude h is proportional to P provided that the temperature is consistent. At 15 degrees Celsius, the pressure is 101.3 pounds per square inch (psi) at sea level and 87.1 psi at height 1000m. Find the pressure ...
*Tuesday, April 28, 2015 by Anonymous*

**Calculus**

Susan pulls on a rope sleigh with a force of 120 N. If the rope makes an angle of 25 degrees with the horizontal, what is the force that tends to lift the sleigh? a)120.00 N b)108.76 N c)50.71 N d)84.85 N how would you know?
*Tuesday, April 28, 2015 by Sara*

**Calculus**

Can someone check my work on this problem? I'm studying for the AP test and I would really appreciate any help. Let f(x) = the definite integral from [-2,(x^2-3x)] of e^(t^2) dt At what value of x is f(x) a minimum? a. For no value of x b. 1/2 c. 3/2 d. 2 e. 3 The answer I...
*Tuesday, April 28, 2015 by ashley*

**Calculus**

Find the area of the largest rectangle that fits inside a semicircle of radius 10 (one side of the rectangle is along the diameter of the semicircle).
*Tuesday, April 28, 2015 by Chris*

**Calculus help??**

I'm not sure how to solve this and help would be great! d/dx [definite integral from 0 to x of (2pi*u) du] is: a. 0 b. 1/2pi sin x c. sin(2pi x) d. cos (2pi x) e. 2pi cos (2pi x) This is the fundamental theorem, right? What's confusing me is the u and du and the end. ...
*Tuesday, April 28, 2015 by ashley*

**Calculus I**

Marketing tells you that if you set the price of an item at $10 then you will be unable to sell it, but that you can sell 500 items for each dollar below $10 that you set the price. Suppose your fixed costs total $3000, and your marginal cost is $2 per item. What is the most ...
*Tuesday, April 28, 2015 by John*

**Differential Calculus**

a person standing at the edge of a cliff throws a rock directly upward. it observed that 2 seconds later, the rock is it maximum height and that 5 seconds after it reached the highest point, it hits the ground at the base of the cliff. what is the initial velocity of the rock
*Tuesday, April 28, 2015 by rex*

**Calculus**

find the area of the region bounded by the curves y=x^2-1 and y =cos(x)
*Monday, April 27, 2015 by joe9*

**Calculus**

find area of the region bounded by the curves y=x^2-1 and y=cos(x). give your answer correct to 2 decimal places.
*Monday, April 27, 2015 by joe9*

**Calculus**

How would I find the second derivative if f(x)= √(x^3+2) using the quotient rule. I got to the step where [(12x√(x^3+2))-(9x^4/√(x^3+2))]/4(x^3+2) how would i go from that to: (3x(x^3+8))/(4(x^3+2)^3/2)
*Monday, April 27, 2015 by Sara*

**calculus check**

Find the limit as x approaches 3 of [(2x^3-5x^2+7)/(3sin(xpi/6)-cos(xpi))] When I plugged in 3, I got 4.
*Sunday, April 26, 2015 by Jeff*

**calculus**

Given the relationship 2x^2 + y^3 =10, with y > 0 and dy, dt = 3 units/min., find the value of dx, dt at the instant x = 1 unit.
*Sunday, April 26, 2015 by Anonymous*

**Calculus 2**

Determine whether the series is convergent, absolutely convergent, conditionally convergent, or divergent. On top of the summation sign (∑) is infinity. Under the summation sign is n=2, and right next to it (to the right of ∑ sign) is (n root of (n)-1)^n (Sorry I ...
*Sunday, April 26, 2015 by Sena*

**Calculus**

Find the average value of f(x) on the interval [-1, 3] when f'(x)=3x^2-6x and f(2)=0.
*Sunday, April 26, 2015 by Anonymous*

**Calculus**

The expression dy/dx = x*(cube root y) gives the slope at any point of the graph of the function f(x) where f(2) = 8. A. Write the equation of the tangent line to f(x) and any point (2,8). B. Write an expression for f(x) in terms of x. C. What is the domain of f(x)? D. What is...
*Sunday, April 26, 2015 by ashley*

**Calculus**

Find limit as x approaches 0 [7x/(sqrt(x+4)-2)]
*Sunday, April 26, 2015 by Anonymous*

**Calculus**

People are entering a zoo at the rate of 100e^t+75t people per hour where t is the amount of time the zoo has been open on that day measured in hours. If the doors are open at 9:00 AM, how many hundreds of people have entered the zoo at 11:40 AM? (Nearest integer)
*Sunday, April 26, 2015 by Sarah*

**calculus**

If f(x)=the integral of (3x^2+2x+4) dx, find C if f(1)=10.
*Sunday, April 26, 2015 by Jeff*

**Calculus**

Find the area bounded by y=x^2-4x+3 and y=x+4 to the newrest integer.
*Sunday, April 26, 2015 by Anonymous*

**Calculus 2**

Use the Comparison Test to determine whether the series is convergent or divergent. On top of the summation sign (∑) is infinity. Under the summation sign is n=1, and right next to it (to the right of ∑ sign) is cos^2n/n^2. How would I compare them and come to the ...
*Saturday, April 25, 2015 by Sena*

**calculus**

A water tank has the shape of an inverted right circular cone with base radius 3 meters and height 6 meters. Water is being pumped into the tank at the rate of 12 meters3/sec. Find the rate, in meters/sec, at which the water level is rising when the water is 2 meters deep. ...
*Saturday, April 25, 2015 by ana*

**Calculus 2**

Determine whether the p-series is convergent or divergent. On top of the summation sign (∑) is infinity. Under the summation sign is n=1, and right next to it (to the right of ∑ sign) is 3/n^e. I was wondering how would you start the problem from start to finish. ...
*Saturday, April 25, 2015 by Sena*

**Pre-Calculus**

Two hoses together fill a pool in 2 h. If only hose A is used, the pool fills in 3 h. How long would it take to fill the pool if only hose B were used? I multiplied 3 and 2 and got 6 hours. Is this a valid method? Thanks
*Saturday, April 25, 2015 by Lucina*

**Calculus**

A circle has a radius lf 10/(pi-1) which is the same value as the side of a square. Both the radius of the circle and the side of the square are gowing at 1 in/sec. Find the difference between the rates of change of their area in in/sec.
*Saturday, April 25, 2015 by Sarah*

**Calculus**

Given f(x)=x^2-27x-28, find the largest integer in shich f is decreasing.
*Saturday, April 25, 2015 by Anonymous*

**Calculus**

A particle moves along the curve y = 3x2 + 1 in such a way that the y value is increasing at the rate of 3 units per second. At what rate is x changing when x = 2?
*Saturday, April 25, 2015 by emma *

**Calc 1**

Consider the following function. f(x) = x^6 ln x (a) Use l'Hospital's Rule to determine the limit as x → 0+. (b) Use calculus to find the minimum value. Find the interval where the function is concave up. (Enter your answer in interval notation.) Find the ...
*Friday, April 24, 2015 by TayB*

**calculus**

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=3 sqrt x,y=3 and 2y+1x=4
*Friday, April 24, 2015 by webworks*

**Pre-Calculus**

Simplify the rational expression and then add or subtract. Express answers in simplest form and identify all non-permissible values. (The non-permissible value is not the issue. It is the simplification) 3x + 15/x^2-25 + 4x^2 -1/ 2x^2 + 9x -5 3(x+5)/(x+5)(x-5) + 4x^2 -1/ (x+5...
*Wednesday, April 22, 2015 by Lucina*

**Calculus Indefinite Intergral**

I need help with integrating these two problems. Im stuck. 1. integrate (sin^-1)dx/((1-x^2)^3/2) sin^-1 aka arcsin 2. integrate dx/((1-x^2)^3/2) by using 1/z Any and all help will be appreciated!
*Wednesday, April 22, 2015 by John*

**Calculus**

(Bees collecting pollen and nectar - Optimization) Many bees collect both pollen and nectar. Pollen is used for protein, and nectar is used for energy. Suppose the amount of nectar harvested during t seconds on a flower is: F(t)=t/(1+t) and that the amount of pollen harvested ...
*Wednesday, April 22, 2015 by Corbin*

**pre-calculus**

eliminate parameters of x=1+cos t y=1-sin t graph the parametric equations
*Wednesday, April 22, 2015 by JK*

**calculus**

In the space below, provide the smaller of the two positive integers that add to 40 and have the largest possible product
*Wednesday, April 22, 2015 by emma *

**calculus**

If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to the nearest square foot without commas. For example, if the answer is 1,000, write 1000.
*Wednesday, April 22, 2015 by emma *

**calculus (please help)**

find the volume of the solid whose bounded by the circle x^2+y^2=4 and whose cross sections perpendicular to the y-axis are isosceles right triangles with one leg in the base. Please give explanation and steps
*Wednesday, April 22, 2015 by may*

**Pre-Calculus**

Can the following be reduced any further? 14x^2/56y^3 I did not reduce because there were different variables in the numerator and denominator. Thanks
*Wednesday, April 22, 2015 by Lucina*

**calculus**

find the area under the curve y= 1/(3x+1)^2 over the interval [0,1]. please show all steps
*Wednesday, April 22, 2015 by Linda*

**Calculus**

F(x)=Integral of (-12sinx/cos^2x) dx+c F(0)=4. Find C
*Wednesday, April 22, 2015 by Anonymous*

**integral calculus**

Integrate with respect to x : ∫3−1x7+x2−−ͨ2;−−√dx
*Wednesday, April 22, 2015 by yomi*

**calculus**

A firework is launched at the rate of 10 feet per second from a point on the ground 50 feet from an observer. To 2 decimal places in radians per second, find the rate of change of the angle of elevation when the firework is 40 feet above the ground. Type your answer in the ...
*Monday, April 20, 2015 by emma *

**Calculus**

A fence 4 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
*Monday, April 20, 2015 by Anonymous*

**math**

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = e^(3t^2) − 3t dt from 4 to x
*Monday, April 20, 2015 by jessica*

**Calculus**

Consider the function f : [-pi,pi] --> R given by f(x) = e^-x*sin(x). (a) Calculate local maxima/minima and points of in ection of f(x).
*Monday, April 20, 2015 by Galagan*

**Calculus check and help**

Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the the area of R. B. Find the value of z so that x=z cuts the solid R into two parts with equal area. C. Find the...
*Sunday, April 19, 2015 by Anonymous*

**Calculus**

Evaluate the integral f sin(x)/1-sin^2(x) dx
*Sunday, April 19, 2015 by joe9*

**Calculus**

Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. The region R is the base of a solid. For this solid, the cross sections, perpendicular to the spx-axis, are rectangles ...
*Sunday, April 19, 2015 by Anonymous*

**Calculus**

Determine the interval on which f(x) = sqrt x-3 is integrable
*Sunday, April 19, 2015 by joe9*

**Calculus**

Give a Right-hand sum approximation of integral 1 to 4 of x^2 with n=4? I have done this problem alot and my teacher says the answer is 30 but I cant get it. HELP
*Sunday, April 19, 2015 by Jason*

**Calculus**

Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the volume of the solid generated when R is revolved around the line y=pi. B. Fine the volume of the solid ...
*Sunday, April 19, 2015 by Anonymous*