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Chapter 1: Q. 26 (page 153)

Find the limit by hand.
$\lim_{x \to \infty} \sin (\tan^{- 1} x)$

Short Answer

Expert verified

On solving the limit, we get, $1$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$\lim_{x \to \infty} \sin (\tan^{- 1} x)$

02

Step 2. Solve the given limit.

Using the limits,

$= \sin (\tan^{- 1} \infty) = \sin (\frac{π}{2}) = 1$

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Most popular questions from this chapter

$\lim_{x \to 1} (\frac{e^{x} - 1}{e^{2 x} + 2 e^{x} - 3})$

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

$lim_{x \to - 2^{+}} (1 + \sqrt{x + 2}) = 1$ find δ in terms of $ε$ .

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.

$\lim_{x \to \infty} \frac{x - 1}{x} = 1$ , find $N$ in terms of $ε$ .

Use what you know about one-sided limits to prove that a function $f$ is continuous at a point $x = c$ if and only if it is both left and right continuous at $x = c$ .

Use the delta-epsilon definition of continuity to argue that f is or is not continuous at the indicated point $x = c$ .

$f (x) = \{\begin{aligned} 2 - x, if x rational \\ x^{2}, if x irrational, \end{aligned} c = 2$

See all solutions

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