Problem to solve
Compute \[ \lim_{ x \to 4^- } \frac{3}{x-4} \]
Solution
STEP 1
Find the following limit: lim_(x->4^-) 3/(x - 4)
STEP 2
Hint: | If neither of the terms of a product approach 0 as x->a, then by the product rule, the limit of the product is the product of the limits. Applying the product rule, write lim_(x->4^-) 3/(x - 4) as 3 lim_(x->4^-) 1/(x - 4): 3 lim_(x->4^-) 1/(x - 4)
STEP 3
Hint: | If lim_(x->4^-) y = 0, then the limit of 1/y is ± ∞. Since lim_(x->4^-)(x - 4) = 0 and x - 4<0 for all x just to the left of x = 4, lim_(x->4^-) 1/(x - 4) = -∞: 3 -∞
STEP 4
Hint: | Evaluate 3 (-∞). 3 (-∞) = -∞: Answer: | | -∞
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Edited by tododemate® - 2021