?Find the limit or show that it does not exist.\(\lim _{x \rightarrow \infty} \frac{3

Chapter 2, Problem 20

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QUESTION:

Find the limit or show that it does not exist.

\(\lim _{x \rightarrow \infty} \frac{3 x^{3}-8 x+2}{4 x^{3}-5 x^{2}-2}\)

Equation Transcription:

Text Transcription:

\lim _{x \rightarrow \infty} \frac{3 x^{3}-8 x+2}{4 x^{3}-5 x^{2}-2}

Questions & Answers

QUESTION:

Find the limit or show that it does not exist.

\(\lim _{x \rightarrow \infty} \frac{3 x^{3}-8 x+2}{4 x^{3}-5 x^{2}-2}\)

Equation Transcription:

Text Transcription:

\lim _{x \rightarrow \infty} \frac{3 x^{3}-8 x+2}{4 x^{3}-5 x^{2}-2}

ANSWER:

Step 1 of 2

The given expression is

The objective of the problem is to obtain the limit.

The quotient rule of limits states that

The sum/difference rule of limits states that .

The constant function rule for limits states that , where  is a constant real number.

The limit to infinity property states that , where  is a positive integer. Also, , where  is any real number and  is a positive integer.

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