find the limit. write ∞ or - ∞ where appropriate. \nlim(x→4⁻) 1/(x - 4)\nlim(x→4⁻) 1/(x - 4)=□ (simplify…

find the limit. write ∞ or - ∞ where appropriate. \nlim(x→4⁻) 1/(x - 4)\nlim(x→4⁻) 1/(x - 4)=□ (simplify your answer.)

find the limit. write ∞ or - ∞ where appropriate. \nlim(x→4⁻) 1/(x - 4)\nlim(x→4⁻) 1/(x - 4)=□ (simplify your answer.)

Answer

Explanation:

Step1: Analyze the left - hand limit

As (x\to4^{-}), it means (x) approaches (4) from the left - hand side. So (x<4), and then (x - 4<0). Let (t=x - 4), as (x\to4^{-}), (t\to0^{-}).

Step2: Evaluate the limit

We have (\lim_{x\to4^{-}}\frac{1}{x - 4}=\lim_{t\to0^{-}}\frac{1}{t}). When (t) approaches (0) from the left - hand side, (\frac{1}{t}) approaches (-\infty).

Answer:

(-\infty)