Which statement best describes the limit shown below? lim_(x rarr oo)(ln x+10x^(20))/(x^(88)+e^(x)) The limit equals zero The limit does not exist The limit exists and does not equal zero

Analyze Behavior: We need to analyze the behavior of the numerator and the denominator as x approaches infinity to determine the limit.Numerator Growth: The numerator ln x + 10x^20 grows without bound as x approaches infinity, but at a much slower rate than x^20 because the logarithmic function grows slower than any polynomial.Denominator Growth: The denominator x^88 + e^x also grows without bound as x approaches infinity. However, e^x grows much faster than any polynomial, including x^88.Comparison of Growth Rates: Since e^x in the denominator grows faster than any term in the numerator, the fraction as a whole approaches zero as x approaches infinity.Limit Conclusion: Therefore, the limit of (ln x + 10x^20) / (x^88 + e^x) as x approaches infinity is 0.

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Which statement best describes the limit shown below?

lim_(x rarr oo)(ln x+10x^(20))/(x^(88)+e^(x))
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? $\newline$ $\lim _{x \rightarrow \infty} \frac{\ln x+10 x^{20}}{x^{88}+e^{x}}$ $\newline$ 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{\ln x+10 x^{20}}{x^{88}+e^{x}}

\newline

The limit equals zero

\newline

The limit does not exist

\newline

The limit exists and does not equal zero

Analyze Behavior: We need to analyze the behavior of the numerator and the denominator as $x$ approaches $\infty$ to determine the limit.
Numerator Growth: The numerator $\ln x + 10x^{20}$ grows without bound as $x$ approaches infinity, but at a much slower rate than $x^{20}$ because the logarithmic function grows slower than any polynomial.
Denominator Growth: The denominator $x^{88} + e^x$ also grows without bound as $x$ approaches infinity. However, $e^x$ grows much faster than any polynomial, including $x^{88}$ .
Comparison of Growth Rates: Since $e^x$ in the denominator grows faster than any term in the numerator, the fraction as a whole approaches zero as $x$ approaches infinity.
Limit Conclusion: Therefore, the limit of $\frac{\ln x + 10x^{20}}{x^{88} + e^x}$ as $x$ approaches infinity is $0$ .