1,125 Answered Questions for the topic AP Calculus
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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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?
what is newtons law of cooling, and how do you apply it?
inputting time, and temperatures
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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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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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If an object is displaced a distance d by a constant force F, the amount of work done is given by _____.
a. W=F+d
b. W=F-d
c. W=Fd
d. W=F/d
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Find the solution of the differential equation
equation: dy/dx=(x+1)/y2 that passes through the point (-2, 2).
a. y=√(1/2 x2+x+4) b. y=3√(3/2 x2 +2)
c. y=3√(3/2 x2+3x+8)
d. y=3√(1/2 x2+x+8)
e. none of these
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Equation to find the amount left after t years
Suppose that a sample initially contains N0 grams of a radioactive substance. If this substance has a half-life of 32 years, then which of the following equations can be used to find the amount...
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Which of these differential equations is NOT seperable?
dy/dy=x+y
dy/dy=xy
dy/dy=x/y
dy/dy=2xy
A tank is formed by revolving the graph of y=x^4 around the y-axis. The tank has a height of 16.
Find the value of m such that the line y = m represents the height at which the tank is half full.
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