Use the differential dV to estimate the change in volume of a sphere when the radius changes from 5 to 4.1. Round answer to nearest tenth if necessary. Recall that the volume of a sphere is 34r3where r is the radius of the sphere.

A cylindrical can has a height of 20cm and a radius of 5cm. The volume of the cylindrical can is decreasing at a rate of 565 cubic cm per second, with the height being held constant. What is the rate of change of the radius in cm per second, when the radius is 5cm?

provide answer in centimeter per second.

Find the following antiderivative 4te3t2dt.

Find dy/dx, where y is defined as a function of x implicitly by this equation: 2y^5-3xy^3=-3.

dy/dx=

Given that q(x) =-6x^3+6x^2-5x-13, find (q^-1)'(4) using the inverse Function Theorem. Note that q(-1) =4.

Find the definite integral23099x28dx Enter an exact answer.

Find the equation of the line tangent to the graph of f(x)=-3 cos (x) at x=2. provide answer in point slope formyy0=m(xx0).

Evaluate the limitlimx1((2x1)22)

Find F'(x) given that F(x) =x24+sin(8t)In(t6)2dt.

F'(x)=

Let h(x)= f(x)-g(x). If F(x)=2x^2 and g(x)=4x, what is h'(4)?

A 90-inch by 240-inch piece of cardboard is used to make an open-top container by removing a square from each corner of the cardboard and folding up the flaps on each side. What is the area of the square that should be cut from each corner to get a container with the maximum volume? Give answer as a simplified fraction or a decimal rounded to four places. Provide answer in square inches.