Chapter 14: Q. 6 (page 907)

In Problems 1– 6, find each limit
$\lim_{x \to \frac{π}{4}} \frac{\tan x}{1 + \cos^{2} x}$

Short Answer

Expert verified

The value is $\frac{2}{3}$

Step by step solution

Step 1. Distributing the limit

The given limit is $\lim_{x \to \frac{π}{4}} \frac{\tan x}{1 + \cos^{2} x}$

It can be written as

$\frac{\lim_{x \to \frac{π}{4}} \tan x}{\lim_{x \to \frac{π}{4}} (1 + \cos^{2} x)}$

Step 2. Value of the limit

On simplifying the limit

$\frac{\lim_{x \to \frac{π}{4}} \tan x}{\lim_{x \to \frac{π}{4}} (1 + \cos^{2} x)} = \frac{\lim_{x \to \frac{π}{4}} \tan x}{\lim_{x \to \frac{π}{4}} 1 + \lim_{x \to \frac{π}{4}} \cos^{2} x} = \frac{\tan (\frac{π}{4})}{\lim_{x \to \frac{π}{4}} 1 + \cos^{2} (\frac{π}{4})} = \frac{\tan (\frac{π}{4})}{1 + \cos^{2} (\frac{π}{4})} = \frac{1}{1 + {(\frac{\sqrt{2}}{2})}^{2}} = \frac{2}{3}$

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In Problems 1– 6, find each limit
$\lim_{x \to \frac{π}{4}} \frac{\tan x}{1 + \cos^{2} x}$

Short Answer

Step by step solution

Step 1. Distributing the limit

Step 2. Value of the limit

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In Problems 1– 6, find each limitlimx→π4tanx1+cos2x

Short Answer

Step by step solution

Step 1. Distributing the limit

Step 2. Value of the limit

One App. One Place for Learning.

Most popular questions from this chapter

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In Problems 1– 6, find each limit
$\lim_{x \to \frac{π}{4}} \frac{\tan x}{1 + \cos^{2} x}$