One-sided limits from graphs

One-sided limits from graphs
Description
Exercise Name:	One-sided limits from graphs
Math Missions:	Precalculus Math Mission, Mathematics III Math Mission Differential calculus Math Mission
'Types of Problems:	2

The One-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 one-sided limits.

Types of Problems

There are two types of problems in this exercise:

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

   

   Select the limit from the list

2. Find the value of the limit: This problem provides the student with a graph of a function. The student is asked to use the graph to determine the one-sided limit and type it in the space provided.

   

   Find the value of the limit

Strategies

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

1. One-sided limits always exist and can possibly be infinite.
2. Use a finger and travel along the curve towards the x-value in the limit from the direction specified in the problem (- is from the left and + is from the right).
3. The y-value is the answer since that is the output (value) of the function.
4. On the Find the value of the limit problem the limit will not be infinity.
5. 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.
2. Calculus has massive applications to physics, chemistry, biology, economics and many other fields.