Exam 1: Limits and Continuity

Find .

For the function f graphed here: , find .

Show that the equation f(x) = x² + 3x - 4 has at least one solution in the interval [-5,0].

Use $\delta$ and $\varepsilon$ to prove .

Find the smallest integer N such that and $\varepsilon$ = 0.000099.

Find .

Determine if the discontinuity at x = 9 in the function is removable.

Answer true or false. The Intermediate-Value Theorem can be used to approximate the locations of all discontinuities for .

Redefine so that it will be continuous everywhere.

Let . Then

Find the limit.

Answer true or false. If and then

Express the right hand limit at x = 2 for .

Let , then

Find .

Convert into a limit as x nears 0.

Find the values of x (if any) at which f is not continuous. f(x) = (x + 8)⁷.

For the function g graphed here, find and identify the function.

On the interval of [-4, 4], where is f not continuous?

Find a value for the constant k so that will be continuous at t = 0.