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 right 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