173 Answered Questions for the topic AP Calculus

11/28/16

A crowd gathers around a movie star, forming a circle.

The radius of the crowd increases at a rate of 6 ft/sec. How fast is the area taken up by the crowd increasing when the radius is 14 ft?    Related Rates of AP Calculus!!!! Please help!!!!

11/28/16

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean.

The radius of the spill increases at a rate of 8 m/min. How fast is the area of the spill increasing when the radius is 8 m?   Related Rates of AP Calculus!!!!Please help!!!!!

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

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

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!!!!

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!!!

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

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

08/09/16

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

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.

07/27/16

Finding domain and range

f(x)= -sqroot x+3

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

04/18/16

deferentiate cos^e^x^2(2x)

How do I derentiate the above equation

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

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

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)

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!

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. 

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?

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?

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)

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

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?

12/27/15

Relative Extrema

 list the relative extrema and inflection points for f(x)=(x3/3)+6x2+1

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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