Which statement best describes the limit shown below? lim_(x rarr oo)(9x^(56))/(-10e^(x)-10x^(97)) The limit equals zero The limit does not exist The limit exists and does not equal zero

Analyze Behavior as x Approaches Infinity: We need to analyze the behavior of the function as x approaches infinity. To do this, we look at the degrees of the polynomial in the numerator and the terms in the denominator.Degree of Numerator and Denominator: The numerator is 9x^(56), which is a polynomial of degree 56. The denominator is -10e^(x)-10x^(97), which contains an exponential function e^(x) and a polynomial of degree 97.Exponential Function Dominance: As x approaches infinity, the exponential function e^(x) grows much faster than any polynomial. Therefore, the term -10e^(x) in the denominator will dominate over the -10x^(97) term.Denominator Grows Faster: Since the exponential function grows faster than any power of x, the denominator will grow much faster than the numerator as x approaches infinity. This means that the fraction as a whole will approach zero.Limit as x Approaches Infinity: Therefore, the limit of (9x^(56))/(-10e^(x)-10x^(97)) as x approaches infinity is 0.

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Which statement best describes the limit shown below?

lim_(x rarr oo)(9x^(56))/(-10e^(x)-10x^(97))
The limit equals zero
The limit does not exist
The limit exists and does not equal zero

Which statement best describes the limit shown below? $\newline$ $\lim _{x \rightarrow \infty} \frac{9 x^{56}}{-10 e^{x}-10 x^{97}}$ $\newline$ The limit equals zero $\newline$ The limit does not exist $\newline$ The limit exists and does not equal zero

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Q. Which statement best describes the limit shown below?

\newline

\lim _{x \rightarrow \infty} \frac{9 x^{56}}{-10 e^{x}-10 x^{97}}

\newline

The limit equals zero

\newline

The limit does not exist

\newline

The limit exists and does not equal zero

Analyze Behavior as $x$ Approaches Infinity: We need to analyze the behavior of the function as $x$ approaches infinity. To do this, we look at the degrees of the polynomial in the numerator and the terms in the denominator.
Degree of Numerator and Denominator: The numerator is $9x^{56}$ , which is a polynomial of degree $56$ . The denominator is $-10e^{x}-10x^{97}$ , which contains an exponential function $e^{x}$ and a polynomial of degree $97$ .
Exponential Function Dominance: As $x$ approaches infinity, the exponential function $e^{x}$ grows much faster than any polynomial. Therefore, the term $-10e^{x}$ in the denominator will dominate over the $-10x^{97}$ term.
Denominator Grows Faster: Since the exponential function grows faster than any power of $x$ , the denominator will grow much faster than the numerator as $x$ approaches infinity. This means that the fraction as a whole will approach zero.
Limit as x Approaches Infinity: Therefore, the limit of $\frac{9x^{56}}{-10e^{x}-10x^{97}}$ as x approaches infinity is $0$ .