Which statement best describes the limit shown below? lim_(x rarr oo)(4e^(x))/(-x^(34)) The limit equals zero The limit does not exist The limit exists and does not equal zero

Analyze Function: Analyze the given function. We are given the function (4e^(x))/(-x^(34)) and we need to find the limit as x approaches infinity. We notice that the numerator grows exponentially with x, while the denominator grows polynomially with a very high degree (34). Compare Growth Rates: Compare the rates of growth of the numerator and the denominator. The exponential function e^(x) grows faster than any polynomial function as x approaches infinity. However, the degree of the polynomial in the denominator is significantly higher than the exponent in the numerator, which suggests that the denominator will eventually outgrow the numerator as x becomes very large. Apply Limits: Apply the concept of limits to the function. As x approaches infinity, the exponential term e^(x) becomes very large, but the polynomial term x^(34) becomes much larger. Since the denominator grows faster than the numerator, the fraction as a whole approaches zero. Conclude Limit: Conclude the limit. The limit of (4e^(x))/(-x^(34)) as x approaches infinity is zero because the denominator's growth rate is much higher than that of the numerator.

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Which statement best describes the limit shown below?

lim_(x rarr oo)(4e^(x))/(-x^(34))
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? $\newline$ $\lim _{x \rightarrow \infty} \frac{4 e^{x}}{-x^{34}}$ $\newline$ 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{4 e^{x}}{-x^{34}}

\newline

The limit equals zero

\newline

The limit does not exist

\newline

The limit exists and does not equal zero

Analyze Function: Analyze the given function. $\newline$ We are given the function $(4e^{x})/(-x^{34})$ and we need to find the limit as $x$ approaches infinity. We notice that the numerator grows exponentially with $x$ , while the denominator grows polynomially with a very high degree ( $34$ ).
Compare Growth Rates: Compare the rates of growth of the numerator and the denominator. $\newline$ The exponential function $e^{x}$ grows faster than any polynomial function as $x$ approaches infinity. However, the degree of the polynomial in the denominator is significantly higher than the exponent in the numerator, which suggests that the denominator will eventually outgrow the numerator as $x$ becomes very large.
Apply Limits: Apply the concept of limits to the function. $\newline$ As $x$ approaches infinity, the exponential term $e^{x}$ becomes very large, but the polynomial term $x^{34}$ becomes much larger. Since the denominator grows faster than the numerator, the fraction as a whole approaches zero.
Conclude Limit: Conclude the limit. $\newline$ The limit of $\frac{4e^{x}}{-x^{34}}$ as $x$ approaches infinity is zero because the denominator's growth rate is much higher than that of the numerator.