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Chapter 1: Q. 4 (page 153)

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

Short Answer

Expert verified

The value of the limit given is $\infty$ .

Step by step solution

Step 1. Given Information.

Given: $\lim_{x \to 1} \frac{1}{x^{2} - 1} .$

Step 2. Calculating the limit using direct substitution.

$S o l v i n g b y h a n d, \lim_{x \to 1} \frac{1}{x^{2} - 1} = \frac{1}{1 - 1} = \frac{1}{0} = \infty .$

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Most popular questions from this chapter

For each functionf graphed in Exercises23–26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

$\lim_{x \to 0} (\frac{2 x}{e^{x} - 1})$

Write delta-epsilon proofs for each of the limit statements $\lim_{x \to c} f (x) = L$ in Exercises $47 - 60$ .

$\lim_{x \to 1} (2 x + 4) = 6$ .

For each limit statement in Exercises $41 - 44$ , use algebra to find $δ$ or $N$ in terms of $ε$ or $M$ , according to the appropriate formal limit definition.

$\lim_{x \to 1^{-}} \frac{1}{1 - x} = \infty$ , find $δ$ in terms of $M$ .

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Calculating limits: Find each limit by hand.limx→11x2-1.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculating the limit using direct substitution.

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Most popular questions from this chapter

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