Question

Consider the function \( f(x)=\frac{x^{2}-49}{x(x-7)} \). a. Evaluate \( \lim _{x \rightarrow \infty} f(x) \) and \( \lim _{x \rightarrow-\infty} f(x) \), and then identify the horizontal asymptotes. b. Find the vertical asymptotes. For each vertical asymptote \( x=a \), evaluate \( \lim _{x \rightarrow a^{-}} f(x) \) and \( \lim _{x \rightarrow a^{+}} f(x) \). a. Evaluate \( \lim _{x \rightarrow \infty} f(x) \). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. \( \lim _{x \rightarrow \infty} \frac{x^{2}-49}{x(x-7)}=\square \) (Simplify your answer.) B. The limit does not exist and is neither \( -\infty \) nor \( \infty \).

          Consider the function \( f(x)=\frac{x^{2}-49}{x(x-7)} \).
a. Evaluate \( \lim _{x \rightarrow \infty} f(x) \) and \( \lim _{x \rightarrow-\infty} f(x) \), and then identify the horizontal asymptotes.
b. Find the vertical asymptotes. For each vertical asymptote \( x=a \), evaluate \( \lim _{x \rightarrow a^{-}} f(x) \) and \( \lim _{x \rightarrow a^{+}} f(x) \).
a. Evaluate \( \lim _{x \rightarrow \infty} f(x) \). Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A. \( \lim _{x \rightarrow \infty} \frac{x^{2}-49}{x(x-7)}=\square \) (Simplify your answer.)
B. The limit does not exist and is neither \( -\infty \) nor \( \infty \).

Consider the function f(x)=(x^2-49)/(x(x-7)).
a. Evaluate limx →∞ f(x) and limx →-∞ f(x), and then identify the horizontal asymptotes.
b. Find the vertical asymptotes. For each vertical asymptote x=a, evaluate limx → a^- f(x) and limx → a^+ f(x).
a. Evaluate limx →∞ f(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A. limx →∞(x^2-49)/(x(x-7))=□ (Simplify your answer.)
B. The limit does not exist and is neither -∞ nor ∞.

Added by Stephen C.

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