Problem to solve
Compute \[ \lim_{ x \to 2 } [\frac{1}{x-2}-\frac{4}{x^2-4}] \]
Solution
STEP 1
Find the following limit: lim_(x->2)(1/(x - 2) - 4/(x^2 - 4))
STEP 2
Hint: | Factor the expression inside the limit. 1/(x - 2) - 4/(x^2 - 4) = 1/(x + 2): lim_(x->2)(1/(x + 2))
STEP 3
Hint: | The limit of a continuous function at a point is just its value there. lim_(x->2) 1/(x + 2) = 1/(2 + 2) = 1/4: Answer: | | 1/4
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Edited by tododemate® - 2021