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Chapter 1: Q. 61 (page 136)

Calculate each of limits:
$\lim_{x \to 1} \frac{1}{\sin^{- 1} x}$ .

Short Answer

Expert verified

The solution for the limit $\lim_{x \to 1} \frac{1}{\sin^{- 1} x}$ is, $\frac{2}{π}$ .

Step by step solution

Step 1. Given Information.

The limit is,

$\lim_{x \to 1} \frac{1}{\sin^{- 1} x}$ .

Step 2. Finding the solution.

$\lim_{x \to 1} \frac{1}{\sin^{- 1} x}$

Inputting $x = 1$ ,

$= \frac{1}{\sin^{- 1} 1} = \frac{1}{\frac{π}{2}} = \frac{2}{π}$

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Most popular questions from this chapter

Calculate each of the limits:

$\lim_{h \to 0} \frac{{(2 + h)}^{2} - 2^{2}}{h}$ .

For each limit statement , use algebra to find δ > 0 in terms of $ε$ > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $ε$ .

$\lim_{x \to 1} (3 x + 8) = 11$

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.

State what it means for a function f to be right continuous at a point x = c, in terms of the delta–epsilon definition of limit.

Use algebra to find the largest possible value of δ or smallest possible value of N that makes each implication true. Then verify and support your answers with labeled graphs.

$If x > N, then |\frac{1}{x^{2}} - 0| < 0.001$

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Calculate each of limits:limx→11sin-1x.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the solution.

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Calculate each of limits:
$\lim_{x \to 1} \frac{1}{\sin^{- 1} x}$ .