1)Using the definition of a derivative, i.e., the limit of the difference quotient, find and the equation of the line tangent to the graph at the given value for
. , .
2)A circle has an initial radius of 50 ft when the radius begins decreasing at a rate of 2 ft/min. What is the rate of change of the area at the instant the radius is 10 ft?
3)Find the derivative of the following functions.
4)Evaluate the following limit.
5)Given , find
6)Use the graph of to answer the following questions.
a)Find the values of x in at which is not continuous. Explain why.
b)Find the values of x in at which is not differentiable. Explain why.
7)Find and simplify .