find each limit. use -∞ or ∞ when appropriate.\nf(x)=\\frac{7x - 7}{(x - 7)^4}\n(a) \\lim_{x\\to7^{-}}f(x)\n(…

find each limit. use -∞ or ∞ when appropriate.\nf(x)=\\frac{7x - 7}{(x - 7)^4}\n(a) \\lim_{x\\to7^{-}}f(x)\n(b) \\lim_{x\\to7^{+}}f(x)\n(c) \\lim_{x\\to7}f(x)\n(a) select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n○a. \\lim_{x\\to7^{-}}f(x)= (simplify your answer.)\n○b. the limit does not exist.

find each limit. use -∞ or ∞ when appropriate.\nf(x)=\\frac{7x - 7}{(x - 7)^4}\n(a) \\lim_{x\\to7^{-}}f(x)\n(b) \\lim_{x\\to7^{+}}f(x)\n(c) \\lim_{x\\to7}f(x)\n(a) select the correct choice below and, if necessary, fill in the answer box to complete your choice.\n○a. \\lim_{x\\to7^{-}}f(x)= (simplify your answer.)\n○b. the limit does not exist.

Answer

Explanation:

Step1: Analyze left - hand limit

Let (x\to7^{-}), then (x - 7\to0^{-}). So ((x - 7)^{4}\to0^{+}) (since it's an even - power), and (7x-7\to7\times7 - 7=42).

Step2: Calculate the limit

(\lim_{x\to7^{-}}\frac{7x - 7}{(x - 7)^{4}}=\frac{42}{0^{+}}=\infty)

Step3: Analyze right - hand limit

Let (x\to7^{+}), then (x - 7\to0^{+}), ((x - 7)^{4}\to0^{+}), and (7x - 7\to42).

Step4: Calculate the right - hand limit

(\lim_{x\to7^{+}}\frac{7x - 7}{(x - 7)^{4}}=\frac{42}{0^{+}}=\infty)

Step5: Analyze the two - sided limit

Since (\lim_{x\to7^{-}}f(x)=\lim_{x\to7^{+}}f(x)=\infty), (\lim_{x\to7}f(x)=\infty)

Answer:

(A) A. (\lim_{x\to7^{-}}f(x)=\infty) (B) (\lim_{x\to7^{+}}f(x)=\infty) (C) (\lim_{x\to7}f(x)=\infty)