1,125 Answered Questions for the topic AP Calculus

11/28/16

A funnel in the shape of an inverted cone is 30 cm deep and has a diameter across the top of 20 cm.
Liquid is flowing out of the funnel at the rate of 12 cm^3/sec. At what rate is the height of the liquid decreasing at the instant when the liquid in the funnel is 20 cm deep?    Related Rates of... more
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11/28/16

Air is escaping from a spherical balloon at the rate of 2 cm^3 per minute.
How fast is the surface area shrinking when the radius is 1 cm? V=4/3piR^3 and S=4piR^2 where V is the volume and S is the surface area, R is the radius.       Related Rates of AP Calculus!!!... more
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11/28/16

A person 2 m tall walks towards a lamppost on level ground at a rate of 0.5 m/sec.
The lamp on the post is 5 m high. How fast is the length of the persons shadow decreasing when the person is 3 m from the post?   Related Rates of AP Calculus!!! Please help!!!!
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Ap Calculus Calculus

11/28/16

A conical cup is 4 cm accross and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm^3/sec.
How fast is the water level dropping when the height of the water is 3 cm?     Related Rates of AP Calculus!!!Please help!!!
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Ap Calculus Calculus

11/28/16

A light is on the ground 20 m from a building. A man 2 m tall walks from the light firectly toward the building at 1 m/s.
How fast is the length of his shadow on the building changing when he is 14 m from the building?       Related Rates of AP Calculus!!! Please help!!!
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Ap Calculus Calculus

11/28/16

An airplane is flying towards a radar station at a constant height of 6 km above the ground.
If the distance s between the airplane and the radar station is decreasing at a rate of 400 km per hour when s=10 km, what is the horizontal speed of the plane?       Related Rates of AP... more
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Ap Calculus

11/05/16

How would you change a partition if n=2...and how would you change the partition for a semi-circle if n=2 also? (this for AP Calculus).?
In AP Calculus, we are doing an Introduction to Integration and the Rectangle Approximation Method....and for hw the teacher ask us how would we change the partition if we had n=2, n=8 and... more
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Ap Calculus

08/02/16

The hypotenuse of a right triangle is 3 times as long as the shorter leg. Find the measure of the angle between the shorter leg and the hypotenuse.
Its a word problem for applying inverse trigonometric functions.
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Ap Calculus

07/27/16

Finding domain and range
f(x)= -sqroot x+3
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07/20/16

Use the intermediate value theorem to prove that the equation x^3=x+8 has at least one solution
Use the intermediate value theorem to prove that the equation x^3=x+8 has at least one solution
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Ap Calculus

04/18/16

deferentiate cos^e^x^2(2x)
How do I derentiate the above equation
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Ap Calculus Calculus Ap Calc

02/07/16

Calculus integration question
The rate of depreciation dV / dt of a machine is inversely proportional to the square of t + 1, where V is the value of the machine t years after it was purchased. The initial value of the machine... more
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Ap Calculus Calculus Ap Calc

02/07/16

Use the differential equation and the given point to find the equation of the function. (give your answer correct to three decimal points)
The given point is (-1,3).   The differential is dy/dx= -30/(4x+1)3
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Ap Calculus Calculus Ap Calc

02/07/16

Find F as a function of x
The question states:    F(x)= int_1^x(t3+7t-6)dt   ( F(x) is the integral of (t3+7t-6)dt from x to 1)
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Ap Calculus Calculus Ap Calc

02/07/16

Determine the area under the given curve
The equation is 1/(x8). The limits are x=1 and x=2. I put this into my graphing calculator and it gave me an answer of 0.142 but the answer is not right apparently. Please help!
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Ap Calculus Calculus

02/07/16

Use upper and lower sums to approximate the area under the curve using 7 sub intervals.
The equation is y=sqrt(1-x2). The picture is a concave down curve that goes to 1 in both the y and x direction. I found the lower sum to be 0.6985 but I can not seem to get the uppper sum correct. 
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Ap Calculus

01/12/16

integral question
If ∫ 52  f(x) dx=4 and ∫72 f(x)=-3 then ∫57 f(x)dx=   I got 7 and then redid it and got 12. am I missing something? Whats the right answer?
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Ap Calculus

01/12/16

Average value on Interval
The average value of f(x) = xsinx2  on the interval [(√pi)/2, √pi] is...   I got 2+sqr2/4. is that right?
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Ap Calculus

01/12/16

Integration
How do I solve this? iv have gotten like 3 different answers. Evaluate the following expression by writing it as a definite integral. lim x→∞ ∑n k=1 [4+(2k/n)]2 (2/n)
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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
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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... 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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