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Find the area of the region bounded by y=-x^3+3, y=x, x=-1 and x=1

Find the average value of the function f(x)=x^3 over the interval [0,2] and find the value(s) of x at which the function assumes the average values

find the particular solution of the differential equation f"(x)=6(x-1) whose graph passes through the point (2,1) and is tangent to the line 3x-y-=0 at that point

The pulley is 5ft above the height at which the rope is attached to the boat. If R(t) represents the length of the rope between the boat and the pulley, determine the value of R'(t) at the moment...

I can't figure out how to differentiate this function. Any help would be appreciated. y=ln(x9(sin(x))2) Find y'(x)=

f'(s)=10s-12s3,f(3)=2   f"(x)=sinx,f'(0)=1,f(0)=6

Use the upper and lower sums of 8 rectangles to find the two approximations of the area between f(x)√x+2 and the x-axis over the interval [0,2]   The square root is only over the...

use sigma notation to write the sum 9/(i+1)+9/(i+2)+9/(i+3)+....+9/(i+14)

Time(seconds) .75 | 1.5 | 2 | 2.25 | 2.75 | 3.5 Height(feet) 108 | 119 | 116| 112 | 97 | 59 1. What type of function best models this data linear exponential quadratic or other...

1. f(x)=3x2 -3 2. g(x)= 1/9x2 3. h(x)= -x2 ive tried to do this multiple times and I feel like I keep getting the table wrong which prohibits me from finishing the questions. I...

A building is to be built and will take the form of a semicircular shape and will have a rectangular doorway. The building will be 6 m long and the door must be at least 1 m vertically from the roof...

A building is to be built and will take the form of a semicircular shape and will have a rectangular doorway. The building will be 6 m long and the door must be at least 1 m vertically from the roof...

A particle is moving with velocity v(t) = t^2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position...

A particle is moving with velocity v(t) = t^2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position...

A building is to be built and will take the form of a semicircular shape and will have a rectangular doorway. The building will be 6 m long and the door must be at least 1 m vertically from the roof...

1. f(x)=3x2 -3 2. g(x)= 1/9x2  3. h(x)= -x2   ive tried to do this multiple times and I feel like I keep getting the table wrong which prohibits me from finishing the questions...

Any mention of the logarithm function within this problem will invalidate the part of the answer where it appears. Let G(x) be the function defined by G(x):= Area under the curve f(t) = 1/t, between...

This is a Calculus Question. Please show work if possible

The is a calculus problem. Find the derivative of a trigonometric function