Chapter 14: Q. 35 (page 883)

In Problems 7– 42, find each limit algebraically.
$\lim_{x \to - 1} \frac{{(x + 1)}^{2}}{x^{2} - 1} .$

Short Answer

Expert verified

The answer is 0.

Step by step solution

Step. 1 Given Information

Firstly, we check whether the given function is in indeterminant form or not.

$f (x) = \frac{{(x + 1)}^{2}}{x^{2} - 1}$

Put $x = - 1$ in the numerator we get,

${(x + 1)}^{2} = {(- 1 + 1)}^{2} = 0$ .

Put $x = - 1$ in the denominator we get,

$x^{2} - 1 = {(- 1)}^{2} - 1 = 1 - 1 = 0$ .

Since both numerator and denominator gives 0 means they both have $x = - 1$ as their common root.

Step. 2 Factorizing

Denominator, $x^{2} - 1 = (x + 1) (x - 1) .$

Numerator , ${(x + 1)}^{2} = (x + 1) (x + 1) .$

So,

$\lim_{x \to - 1} \frac{{(x + 1)}^{2}}{x^{2} - 1} = \lim_{x \to - 1} \frac{(x + 1) (x + 1)}{(x + 1) (x - 1)} = \lim_{x \to - 1} \frac{x + 1}{x - 1} .$

Now we can put the limit directly.

Step. 3 Final calculation of the limit

$\lim_{x \to - 1} \frac{x + 1}{x - 1} = \frac{- 1 + 1}{- 1 - 1} = \frac{0}{- 2} = 0 .$

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In Problems 7– 42, find each limit algebraically.
$\lim_{x \to - 1} \frac{{(x + 1)}^{2}}{x^{2} - 1} .$

Short Answer

Step by step solution

Step. 1 Given Information

Step. 2 Factorizing

Step. 3 Final calculation of the limit

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In Problems 7– 42, find each limit algebraically.limx→-1x+12x2-1.

Short Answer

Step by step solution

Step. 1 Given Information

Step. 2 Factorizing

Step. 3 Final calculation of the limit

One App. One Place for Learning.

Most popular questions from this chapter

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In Problems 7– 42, find each limit algebraically.
$\lim_{x \to - 1} \frac{{(x + 1)}^{2}}{x^{2} - 1} .$