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Chapter 14: Q. 4 (page 905)

find the limit $\lim_{x \to 1^{-}} \sqrt{1 - x^{2}}$

Short Answer

Expert verified

$\lim_{x \to 1^{-}} \sqrt{1 - x^{2}} = 0$

Step by step solution

01

Step 1. Given information

$\lim_{x \to 1^{-}} \sqrt{1 - x^{2}}$

02

Step 2. Limit of the function

We can find limit of root function by $\lim_{x \to c} f (x) = f (c)$ if c is in the domain of f(x) and the domain of f(x)= $\sqrt{1 - x^{2}}$ is [-1,1]. So here c is -1 and it is in the domain. So we can use the above formula .

$\lim_{x \to 1} f (x) = f (1) = \sqrt{1 - (1)^{2}} = 0$

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Most popular questions from this chapter

In Problems 43-52, find the limit as $x$ approaches $c$ of the average rate of change of each function from $c$ to $x$ .

$c = 1; f (x) = \frac{1}{x}$

In Problems 7– 42, find each limit algebraically

$\lim_{x \to - 2} (5 x)$

In Problems 13–32, use the accompanying graph of y = f(x).

Find $\lim_{x \to - 6^{-}} f (x) .$

In Problems 53-56, use the properties of limits and the facts that

$\lim_{x \to 0} \frac{\sin x}{x} = 1 \lim_{x \to 0} \frac{\cos x - 1}{x} = 0 \lim_{x \to 0} \sin x = 0 \lim_{x \to 0} \cos x = 1$

$\lim_{x \to 0} \frac{\sin (2 x)}{x}$

Use the graph shown to determine if the limit exists. If it does, find its value.

See all solutions

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