Problem to solve
Compute \[ \lim_{ x \to 4 } \frac{x^2-x-12}{x-4} \]
Solution
STEP 1
Find the following limit: lim_(x->4) (x^2 - x - 12)/(x - 4)
STEP 2
Hint: | Factor the numerator and denominator. (x^2 - x - 12)/(x - 4) = ((x - 4) (x + 3))/(x - 4): lim_(x->4) ((x - 4) (x + 3))/(x - 4)
STEP 3
Hint: | Cancel terms. ((x - 4) (x + 3))/(x - 4) = x + 3: lim_(x->4)(x + 3)
STEP 4
Hint: | The limit of a continuous function at a point is just its value there. lim_(x->4)(x + 3) = 4 + 3 = 7: Answer: | | 7
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Edited by tododemate® - 2021