1,131 Answered Questions for the topic AP Calculus

Ap Calculus

12/27/15

Area Question!
A left sum ad a right sum are used to estimate the area between the graph of the function f(x)=sinx and the x axis from x=0 to x=1.5 Which of the two sum gives an underestimate of the value of the... more
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Ap Calculus

12/23/15

Rolle's Theorem & Second Derivative Test Question
Okay, so when going over some problems to prepare for a test that is coming up soon, I have these two questions im not sure on. I know these types of questions will be on the test, so I need help... more
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Ap Calculus

12/23/15

Applications of Differentiation
A function f is continuous on the closed interval [-3, 3] such that f(-3)=4 and f(3)=1. The function f' and f'' have the following properties:     x:    -3<x<-1      x=-1        ... more
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Ap Calculus

12/22/15

Applications of differentiation
f(x)= sin(x)+1 for the closed interval [0, pi/2] find the value of x to at least 3 decimal places where the average rate of change of the function equals the instantaneous rate of change of the... more
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Ap Calculus

12/18/15

Concavity and second derivative
I am having issues with the following two problems:   Find the critical number of f, describe the open intervals on which f is increasing or decreasing and locate all relative extrema... more
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Ap Calculus

12/18/15

concavity and second derivative
on the interval [-6,6] f(x) is continuous and differentiable. If f'(x)= (x2-4)(x+1) briefly justify the following conclusion:   "f'(x) has an x intercept at x=-1 but x=-1 is not a relative... more
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Ap Calculus

12/05/15

derivatives
how do I find d/dx f(x) if f(x)=3x^2 ?
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Ap Calculus Trigonometry

10/08/15

For what values of x on the interval (0,pi) does the graph of f(x)=cotx+4x have horizontal tangents.
Thank you so much
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Ap Calculus

10/08/15

Find equations of the tangent lines to the graph of f(x)= x/x+2 that are parallel to the line x-2y=1
Can someone please help. Thank you.
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Ap Calculus Math Math Help Calculus 1

08/28/15

What is the limit of (x)/(sin (3x)) as x approaches 0?
I had to solve it by using a calculator but I was wondering, is there a way to solve this analytically? Just wondering, in case it pops up on a no-calculator test.   Thanks a bunch!
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Ap Calculus Calculus Graph Area

08/23/15

the area of the region bounded by y=x^2 and y=x is________.
a. 1/6 b. 1/3 c. 1/2 d. 5/6 e. 1
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Ap Calculus Math Calculus Ap Calc

08/22/15

Suppose we have a rod that is 6 meters long, with density function p(x)=2x+3. What is the center of the mass of the rod?
¯x= 11/3 ¯x= 8/3 ¯x= 14/3 ¯x= 4/3 none of these
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Ap Calculus Math Calculus Ap Calc

08/22/15

probability and integrals
Suppose that f(x) is the probability density function describing the distribution for the number of minutes it takes to solve a puzzle. Which of the following represents the probability that you... more
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08/22/15

differential equation
Suppose that 120 deer are placed in a protected region. If the region can support a maximum deer population of 500, then the bounded growth model for the deer population gives us which differential... more
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Ap Calculus Math Calculus Physics

08/22/15

center mass of a rod
If you have a rod of length 5 with density p(x)=2+(x/5). What is the center of mass of the rod? a. ¯x=2.5 b. ¯x=2.667 c. ¯x=3.333 d. ¯x=2.165
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Ap Calculus Math Calculus Physics

08/22/15

work due to gravity
The force pulling an object to earth is  where G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and r is the distance between the object and the center of... more
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Ap Calculus Math Calculus Ap Calc

08/22/15

A tank is made in the shape of a paraboloid formed by rotating the graph of x^2 about the y-axis from x = 0 to x = 2.
 The tank is filled with a liquid whose density is 30 lb/ft3. Find the work done in pumping the liquid to a level of 15 ft above the top of the tank. a. 34295Π ft-lb b. 3920Π ft-lb ... more
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Ap Calculus Math Calculus Ap Calc

08/22/15

A cylindrical water tower 10 ft in diameter and 40 ft in height has its center 100 ft above the ground.
 A pump on the ground fills the tank with water whose density is 62.4 lb/ft3.   How much work is done in filling the tank half way? a. 35.2 million ft-lb b. 15.7 million ft-lb c. 8.8 million... more
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Ap Calculus Math Calculus Ap Calc

08/22/15

newtons law of cooling
A cup of coffee at 160° is placed in a room where the temperature is 70°. After 5 minutes, the coffee’s temperature is 112.5°.   Find the temperature of the coffee 10 minutes after it was placed... more
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Ap Calculus Math Calculus Ap Calc

08/22/15

newtons law of cooling
A bowl of soup was brought into a room with an initial temperature of 120°. After 10 minutes, its temperature was 105°. After another 10 minutes, its temperature was 95°. Use Newton’s Law of... more
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Ap Calculus Math Calculus Volume

08/22/15

A solid has a flat base, which is bounded by the graph of y=x^3 and y=vx in the first quadrant only.
Each cross section of the solid perpendicular to the x-axis is the shape of a square. Find the volume of this solid.  a. 5/14 b. 25/126 c. 5/12 d. 47/125
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Ap Calculus Math Calculus Physics

08/20/15

a particle moves along the x-axis with its x coordinate given by the function s(t)=2t^3-21t^2+60t for t=0
what would be the speed when t=3 and how do you find the exact time the particle changes direction?
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Ap Calculus Math Calculus Physics

08/20/15

what is newtons law of cooling, and how do you apply it?
inputting time, and temperatures  
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Ap Calculus Math Calculus Area

08/20/15

how do i go about finding the area of this region?
if the region is bounded by the x-axis, y-axis and the graphs of the equations y=1/(x^2)+1 and y=lnx
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Ap Calculus Math Calculus

08/20/15

if you have a rod length 5 with density p(x)=2+(x/5), how would you go about finding the center mass of the rod?
any suggestions?
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