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 \( \lim _{x \rightarrow a^{+}} f(x) \). \( \lim _{x \rightarrow \infty} \frac{x^{2}-49}{x(x-7)}=1 \) (Simplify your answer.) B. The limit does not exist and is neither \( -\infty \) nor \( \infty \). Evaluate \( \lim _{x \rightarrow-\infty} f(x) \). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. \( \lim _{x \rightarrow-\infty} \frac{x^{2}-49}{x(x-7)}=1 \) (Simplify your answer.) B. The limit does not exist and is neither \( -\infty \) nor \( \infty \). Identify the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, \( \square \) (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is \( \square \) and the bottom asymptote is \( \square \) . (Type equations.)

          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 \( \lim _{x \rightarrow a^{+}} f(x) \).
\( \lim _{x \rightarrow \infty} \frac{x^{2}-49}{x(x-7)}=1 \) (Simplify your answer.)
B. The limit does not exist and is neither \( -\infty \) nor \( \infty \).

Evaluate \( \lim _{x \rightarrow-\infty} f(x) \). Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A. \( \lim _{x \rightarrow-\infty} \frac{x^{2}-49}{x(x-7)}=1 \) (Simplify your answer.)
B. The limit does not exist and is neither \( -\infty \) nor \( \infty \).

Identify the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has one horizontal asymptote, \( \square \)
(Type an equation.)
B. The function has two horizontal asymptotes. The top asymptote is \( \square \) and the bottom asymptote is \( \square \) .
(Type equations.)

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).
limx →∞(x^2-49)/(x(x-7))=1 (Simplify your answer.)
B. The limit does not exist and is neither -∞ nor ∞.

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))=1 (Simplify your answer.)
B. The limit does not exist and is neither -∞ nor ∞.

Identify the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has one horizontal asymptote, □
(Type an equation.)
B. The function has two horizontal asymptotes. The top asymptote is □ and the bottom asymptote is □ .
(Type equations.)

Added by Margaret P.

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