Two-sided limits using advanced algebra | |
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Description | |
Exercise Name: | Two-sided limits using advanced algebra |
Math Missions: | Precalculus Math Mission, Differential calculus Math Mission |
Types of Problems: | 1 |
The Two-sided limits using advanced algebra exercise appears under the Precalculus Math Mission and Differential calculus Math Mission. This exercise explores calculating limits with some advanced algebraic manipulation.
Types of Problems[]
There is one type of problem in this exercise:
- Find the limit using algebra: This problem has a limit of a function approaching a number. The user is expected to find the limit and write the correct answer in the space provided.
Strategies[]
Knowledge of the evaluating functions, factoring polynomials, rationalization, and fractions are encouraged to ensure success on this exercise.
- The first method for solving a limit is to plug in the limiting value for x. If this is defined, the result is the answer.
- The second method for solving limits on this exercise is to factor the numerator and denominator, reduce, and then plug in. The result will be the answer.
- If there is a radical in the limit, multiply by the conjugate in either the numerator or denominator as appropriate to eliminate the radical.
- If there are fractions in the limit, combine fractions with the complex fraction techniques before to assist simplification.
- L'hopital's rule comes later in the standard calculus sequence, but after introduced it can be used to perform this exercise more efficiently.
- A calculator can be used by evaluating the function at a number "very close" to the limiting value.
Real-life Applications[]
- Limits are the foundation for both differential and integral calculus.
- The concept of continuity is rigorously defined via limits.
- Asymptotes of rational functions can be understood more rigorously by looking at them as limits.