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Chapter 1: Q. 16 (page 153)

Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that $k$ is positive.
$\lim_{x \to - \infty} \tan^{- 1} x = - .$

Short Answer

Expert verified

The value of the limit $\lim_{x \to - \infty} \tan^{- 1} x = - \frac{π}{2} .$

Step by step solution

01

Step 1. Given Information.

The given limit function is $\lim_{x \to - \infty} \tan^{- 1} x .$

02

Step 2. Value of the limit.

According to a theorem,

$\lim_{x \to - \infty} \tan^{- 1} x = - \frac{π}{2} .$

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Most popular questions from this chapter

Calculate each of the limits:

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

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

$\lim_{x \to 4} (6 x - 1) = 23$ .

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

$f (x) = \{\begin{aligned} 2 - x, if x rational \\ x^{2}, if x irrational, \end{aligned} c = 1$

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| < $ε$ .

$\lim_{x \to 3} (x^{2} - 6 x + 5) = - 4$

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 $ε$ .

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