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Limits at infinity where x is unbounded
Description
Exercise Name: Limits at infinity where x is unbounded
Math Missions: Differential calculus Math Mission
Types of Problems: 2

The Limits at infinity where x is unbounded exercise appears under the Differential calculus Math Mission. This exercise finds limits when the ${x}$ heads off to positive or negative infinity.

## Types of Problems

There are two types of problems in this exercise:

1. Find the limit to infinity: This problem provides a limit towards positive or negative infinity. The user is asked to find the limit and select it from a multiple choice list.
2. Find the limit from the graph: This problem provides the graph of a function. The user is asked to select an answer regarding the limit of the function towards plus or minus infinity.

## Strategies

Knowledge of limits and horizontal asymptotes are encouraged to ensure success on this exercise.

1. A limit to + or - infinity will hug a horizontal asymptote.
2. The types of functions that can appear are rational (which is found by looking at leading coefficients), radical (which is solved with conjugates) or exponential.
3. The answers to these problems can also be found by using a calculator and plugging in a large number for infinity.

## Real-life Applications

1. Limits are used to define both the derivative and the integral.
2. The concept of infinitesimals (arbitrarily close to) has applications to anything where precise answers are not always practical or possible.
3. These problems explore horizontal asymptotes, which are used to find equilibrium in biological, chemical and economic situations.