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Two-sided limits from graphs
Description
Exercise Name: Two-sided limits from graphs
Math Missions: Precalculus Math Mission, Mathematics III Math Mission, Differential calculus Math Mission
Types of Problems: 1

The Two-sided limits from graphs exercise appears under the Precalculus Math Mission, Mathematics III Math Mission and Differential calculus Math Mission. This exercise introduces and practices various kinds of two-sided limits.

## Types of Problems

There is one type of problem in this exercise:

1. Select the limit from the list: This problem provides the user with a graph of a function. The user is asked to use the graph to determine the one-sided limit and make the correct selection from a multiple choice list.

## Strategies

Knowledge and comfort with reading functions from graphs would ensure success on this exercise.

1. Dependent on the textbook used, a two-sided limit cannot be infinite, but it can possibly not exist.
2. Use a finger and travel along the curve towards the x-value in the limit from both directions. They need to be the same for the limit to exist.
3. The y-value is the answer since that is the output (value) of the function.
4. Occasionally the function will be given also a rule ${f(x)}$. If so, it is possible to find the answer and select it before the graph loads.

## Real-life Applications

1. Limits are the foundation of the definition for both the derivative and the integral from calculus.