Math  /  Calculus

QuestionMy score: 7.58/107.58 / 10 pts ( 75.83%75.83 \% ) Evaluate limxf(x)\lim _{x \rightarrow \infty} f(x) and limxf(x)\lim _{x \rightarrow-\infty} f(x) for the following function. Then give the horizontal asymptote(s) of ff (if any). f(x)=2x3+84x3+64x6+3f(x)=\frac{2 x^{3}+8}{4 x^{3}+\sqrt{64 x^{6}+3}}
Evaluate limxf(x)\lim _{x \rightarrow \infty} f(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. limxf(x)=16\lim _{x \rightarrow \infty} f(x)=\frac{1}{6} (Type an integer or a simplified fraction.) B. The limit does not exist and is neither \infty nor -\infty.
Evaluate limxf(x)\lim _{x \rightarrow-\infty} f(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. limxf(x)=\lim _{x \rightarrow-\infty} f(x)=\square (Type an integer or a simplified fraction.) \square B. The limit does not exist and is neither \infty nor -\infty.

Studdy Solution
Determine the horizontal asymptotes based on the limits.
Since both limxf(x) \lim_{x \to \infty} f(x) and limxf(x) \lim_{x \to -\infty} f(x) are equal to 13 \frac{1}{3} , the horizontal asymptote is:
y=13 y = \frac{1}{3}
Solution: - The limit as x x \to \infty is 13 \frac{1}{3} . - The limit as x x \to -\infty is 13 \frac{1}{3} . - The horizontal asymptote of f f is y=13 y = \frac{1}{3} .

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