1,134 Answered Questions for the topic AP Calculus
Ap Calculus
01/12/16
Integral question
let ∫ f(g(x))g'(x) = ∫ (sec2xtan2x)dx.
Identify u=g(x) and du = g'(x)x.
Do not evaluate the integral
Ap Calculus Algebra
01/03/16
What is the difference between rates of change you found in Algebra and rates of change you find in Calculus?
What is the difference between rates of change you found in Algebra and rates of change you find in Calculus?
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Ap Calculus
12/27/15
Relative Extrema
list the relative extrema and inflection points for f(x)=(x3/3)+6x2+1
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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...
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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...
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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 ...
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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...
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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...
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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...
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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.
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!
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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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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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...
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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...
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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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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...
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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
...
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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...
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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...
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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...
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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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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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