Which statement best describes the limit shown below? lim_(x rarr oo)(-10x^(13))/(-2x^(2)) The limit equals zero The limit does not exist The limit exists and does not equal zero

Simplify expression: We are given the limit expression: lim_(x → ∞)(-10x^(13))/(-2x^(2)) First, we simplify the expression by dividing both the numerator and the denominator by x^(2), the highest power of x in the denominator.Further simplification: The simplified expression becomes: lim_(x → ∞)(-10x^(13-2))/(-2) This simplifies to: lim_(x → ∞)(-10x^(11))/(-2)Divide coefficients: Now we can further simplify the expression by dividing the coefficients: lim_(x → ∞)(-10/-2)x^(11) This simplifies to: lim_(x → ∞)5x^(11)Approaching infinity: As x approaches infinity, the term 5x^(11) will also approach infinity since any positive power of x will grow without bound as x becomes larger and larger. Therefore, the limit of 5x^(11) as x approaches infinity is infinity.Final statement: Since the limit of the function as x approaches infinity is infinity, the correct statement is: ＂The limit exists and does not equal zero.＂

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which statement best describes the limit shown below?

lim_(x rarr oo)(-10x^(13))/(-2x^(2))
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? $\newline$ $\lim _{x \rightarrow \infty} \frac{-10 x^{13}}{-2 x^{2}}$ $\newline$ The limit equals zero $\newline$ The limit does not exist $\newline$ The limit exists and does not equal zero

View step-by-step help

Full solution

Q. Which statement best describes the limit shown below?

\newline

\lim _{x \rightarrow \infty} \frac{-10 x^{13}}{-2 x^{2}}

\newline

The limit equals zero

\newline

The limit does not exist

\newline

The limit exists and does not equal zero

Simplify expression: We are given the limit expression: $\newline$ $\lim_{x \to \infty}\frac{-10x^{13}}{-2x^{2}}$ $\newline$ First, we simplify the expression by dividing both the numerator and the denominator by $x^{2}$ , the highest power of $x$ in the denominator.
Further simplification: The simplified expression becomes: $\newline$ $\lim_{x \to \infty}(\frac{-10x^{13-2}}{-2})$ $\newline$ This simplifies to: $\newline$ $\lim_{x \to \infty}(\frac{-10x^{11}}{-2})$
Divide coefficients: Now we can further simplify the expression by dividing the coefficients: $\newline$ $\lim_{x \to \infty}(\frac{-10}{-2})x^{11}$ $\newline$ This simplifies to: $\newline$ $\lim_{x \to \infty}5x^{11}$
Approaching infinity: As $x$ approaches infinity, the term $5x^{11}$ will also approach infinity since any positive power of $x$ will grow without bound as $x$ becomes larger and larger. $\newline$ Therefore, the limit of $5x^{11}$ as $x$ approaches infinity is infinity.
Final statement: Since the limit of the function as $x$ approaches $\infty$ is $\infty$ , the correct statement is: $\newline$ ＂The limit exists and does not equal $0$ .＂