Finding Limits: A Numerical and Graphical Approach
For the following exercises, use Figure 1.
At what values of is the function discontinuous? What condition of continuity is violated?
Using Table 1, estimate
For the following exercises, with the use of a graphing utility, use numerical or graphical evidence to determine the left- and right-hand limits of the function given as approaches If the function has limit as approaches state it. If not, discuss why there is no limit.
Finding Limits: Properties of Limits
For the following exercises, find the limits if and
For the following exercises, evaluate the limits using algebraic techniques.
For the following exercises, use numerical evidence to determine whether the limit exists at If not, describe the behavior of the graph of the function at
For the following exercises, determine where the given function is continuous. Where it is not continuous, state which conditions fail, and classify any discontinuities.
For the following exercises, find the average rate of change
For the following exercises, find the derivative of the function.
Find the equation of the tangent line to the graph of at the indicated value.
For the following exercises, with the aid of a graphing utility, explain why the function is not differentiable everywhere on its domain. Specify the points where the function is not differentiable.
Given that the volume of a right circular cone is and that a given cone has a fixed height of 9 cm and variable radius length, find the instantaneous rate of change of volume with respect to radius length when the radius is 2 cm. Give an exact answer in terms of