Find the  x- values (if any) at which is not continuous.  ​

Discuss the continuity of the function . ​

A ring has a inner circumference of 11 centimeters. If the ring’s inner circumference can vary between 10.5 centimeters  and 12.5 centimeters  how can the radius vary? Round your answer to five decimal places. ​

Find the vertical asymptotes (if any) of the function . ​

Use the graph to determine the following limits, and discuss the continuity of the function at x = -3. (i) (ii) (iii) ​

Complete the table and use the result to estimate the limit.   –0.1 –0.01 –0.001 0.001 0.01 0.1 ​

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. ​ A cyclist is riding on a path whose elevation is modeled by the function wherexand are measured in miles. Find the rate of change of elevation when x= 3.

Find the  x -values (if any) at which the function is not continuous. Which of the discontinuities are removable? ​

Find the value of c guaranteed by the Intermediate Value Theorem. ​ ​

Let and . Find the limit. ​ ​