Limits at infinity where f(x) is unbounded

The  exercise appears under the Differential calculus Math Mission. This exercise finds limits when the function values go to infinity or negative infinity

Types of Problems
There are three types of problems in this exercise:


 * 1) Find the limit of the expression: This problem provides an expression that involves a possible infinite limit. The student is asked to find the limit of the function and select it from the list.Laiwfxiu1.png
 * 2) Find the limit from the graph: This problem provides a graph with multiple vertical asymptotes and other features. The student is asked to find a specific limit and select it from a multiple choice list or write it in the space provided.Laiwfxiu2.png
 * 3) Tell where there are vertical asymptote(s): This problem has a rational function provided. The student is asked to determine if the function has any vertical asymptotes, or if any discontinuities are removable.Laiwfxiu3.png

Strategies
Knowledge of limits and vertical asymptotes are encouraged to ensure success on this exercise.
 * 1) The most common place a function will be unbounded at vertical asymptotes.
 * 2) The + and the - on the limits indicate the direction from which one should head to the x value.
 * 3) Vertical asymptotes occur when the denominator of a rational function is zero after simplification. On this exercise a function should be simplified before finding the vertical asymptotes.

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 vertical asymptotes, commonly associated with logarithms and rational functions.