Exam 1: Limits and Continuity

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

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

First rationalize the numerator, then find the limit.

Use the fact that is a solution of x⁴ - 2 = 0 to approximate with an error of at most 0.005.

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

Find any points of discontinuity for .

Find .

In , determine if the discontinuity at x = 2 is removable.

Find .

The function f(x) is shown in the graph: Find

Find $\delta$ if and $\varepsilon$ = 0.03.

Consider the function f graphed here: For what values of a does exist?

For the function f graphed here: find

Approximate by evaluating -5x⁴ at appropriate values of x.

Find the point of discontinuity in and state whether it is removable.

Find $\delta$ if and $\varepsilon$ = 0.02.

Find .

Find .

To prove that a reasonable relationship between $\delta$ and $\varepsilon$ would be

For the function h graphed here: find