Chapter 1: Q. 6 (page 153)

Calculating limits: Find each limit by hand.
$\lim_{x \to - \infty} \frac{x^{3} + 2 x + 1}{1 - x^{4}} .$

Short Answer

Expert verified

The answer of the limit is 0.

Step by step solution

Step 1. Given Information.

Given: $\lim_{x \to - \infty} \frac{x^{3} + 2 x + 1}{1 - x^{4}}$ .

Step 2. Calculating the limit using direct substitution.

$S o l v i n g b y h a n d, \lim_{x \to - \infty} \frac{x^{3} + 2 x + 1}{1 - x^{4}} D i v i d i n g b o t h n u m e r a t o r a n d d e n o m i n a t o r b y x^{4} . = \lim_{x \to - \infty} \frac{\frac{1}{x} + \frac{2}{x^{3}} + \frac{1}{x^{4}}}{\frac{1}{x^{4}} - 1} = \frac{\frac{1}{\infty} + \frac{2}{\infty} + \frac{1}{\infty}}{\frac{1}{\infty} - 1} = \frac{0 + 0 + 0}{0 - 1} = 0 .$

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Calculating limits: Find each limit by hand.
$\lim_{x \to - \infty} \frac{x^{3} + 2 x + 1}{1 - x^{4}} .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculating the limit using direct substitution.

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Calculating limits: Find each limit by hand.limx→-∞x3+2x+11-x4.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculating the limit using direct substitution.

One App. One Place for Learning.

Most popular questions from this chapter

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Calculating limits: Find each limit by hand.
$\lim_{x \to - \infty} \frac{x^{3} + 2 x + 1}{1 - x^{4}} .$