Techniques for Computing Limits Flashcards
What is the direct substitution method for computing limits?
How can factoring be used to compute limits?
What is the rationalizing technique for limits?
Rationalizing involves multiplying the numerator and denominator by the conjugate when dealing with limits involving square roots. This can simplify the expression and resolve indeterminate forms.
How does finding a common denominator help in computing limits?
When dealing with limits involving fractions, combining terms over a common denominator can simplify the expression, making it easier to evaluate the limit.
How is the Squeeze Theorem used to compute limits?
What is L’Hôpital’s Rule and when is it used?
How do you compute limits as 𝑥 approaches infinity?
For rational functions, divide every term by the highest power of 𝑥 in the denominator, then simplify. The limit as 𝑥 approaches infinity depends on the degrees of the polynomial in the numerator and denominator.
How are limits computed for piecewise functions?
Compute the limit separately for each piece of the function as 𝑥 approaches the point of interest. The overall limit exists if the limits from both sides agree.
How do you determine if a function has a vertical asymptote?
What is algebraic simplification and how is it used in computing limits?
Algebraic simplification involves simplifying the function by expanding, combining like terms, or canceling factors before applying the limit. This can often resolve indeterminate forms.
