Chapter 1: Q. 100 (page 137)

Use the composition rule for limits and the fact that $\tan x$ is continuous on its domain to prove that $\tan^{- 1} x$ is continuous everywhere.

Short Answer

Expert verified

It is proved that $\tan^{- 1} x$ is continuous on its domain.

Step by step solution

Step 1. Given Information

We are given that $\tan x$ is continous.

Step 2. Proving the statement

Using composition rule,

If $x = c$ is in the domain of $\tan x$ .

So, $\lim_{x \to c} \tan x = \tan c$ is the composition given by,

$\lim_{x \to c} \tan (\tan^{- 1} x) = \tan (\lim_{x \to c} \tan^{- 1} x) = \tan (\tan^{- 1} c)$

Hence, $\tan^{- 1} c$ is continous.

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Use the composition rule for limits and the fact that $\tan x$ is continuous on its domain to prove that $\tan^{- 1} x$ is continuous everywhere.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proving the statement

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Use the composition rule for limits and the fact that tanx is continuous on its domain to prove that tan-1x is continuous everywhere.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proving the statement

One App. One Place for Learning.

Most popular questions from this chapter

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Use the composition rule for limits and the fact that $\tan x$ is continuous on its domain to prove that $\tan^{- 1} x$ is continuous everywhere.