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Limits at infinity where f(x) is unbounded
Limits-at-infinity-where-f-x--is-unbounded 256
Description
Exercise Name: Limits at infinity where f(x) is unbounded
Math Missions: Differential calculus Math Mission
'Types of Problems: 3

The Limits at infinity where f(x) is unbounded 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

    Find the limit of the expression

  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

    Find the limit from the graph

  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

    Tell where there are vertical asymptote(s)

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 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.