Limits at infinity where x is unbounded | |
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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 heads off to positive or negative infinity.
Types of Problems[]
There are two types of problems in this exercise:
- 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.
- 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.
- A limit to + or - infinity will hug a horizontal asymptote.
- 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.
- The answers to these problems can also be found by using a calculator and plugging in a large number for infinity.
Real-life Applications[]
- Limits are used to define both the derivative and the integral.
- The concept of infinitesimals (arbitrarily close to) has applications to anything where precise answers are not always practical or possible.
- These problems explore horizontal asymptotes, which are used to find equilibrium in biological, chemical and economic situations.