Q. 85 Use the Squeeze Theorem to find ... [FREE SOLUTION]

91影视

Chapter 1: Q. 85 (page 136)

Use the Squeeze Theorem to find each of the limits in Exercises. Explain exactly how the Squeeze Theorem applies in each case.
$\lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x}$

Short Answer

Expert verified

The limit of the equation $\lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x}$ is 0

Step by step solution

Step 1. Given Information:

$\lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x}$

Step 2. Applying Squeeze theorem on the limit:

By applying the Squeeze theorem;

$R a n g e o f \tan^{- 1} \frac{1}{x} " o r \tan^{- 1} x " i s (- \frac{蟺}{2}, \frac{蟺}{2}) - \frac{蟺}{2} < \tan^{- 1} \frac{1}{x} < \frac{蟺}{2} N o w m u l t i p l y i n g x o n a l l s i d e; - \frac{蟺}{2} x < x \tan^{- 1} \frac{1}{x} < \frac{蟺}{2} x A p p l y i n g l i m i t s o n b o t h s i d e a s x 鈫� 0; \lim_{x 鈫� 0} - \frac{蟺}{2} x < \lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x} < \lim_{x 鈫� 0} \frac{蟺}{2} x - \frac{蟺}{2} (0) < \lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x} < \frac{蟺}{2} (0) 0 < \lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x} < 0 s o, \lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x} = 0$

Step 3. Proving lim x→0x tan-11x=0

$\lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x} \lim_{x 鈫� 0} \frac{\tan^{- 1} \frac{1}{x}}{\frac{1}{x}} U \sin g L' H o s p i t a l' s R u l e : \lim_{x 鈫� 0} \frac{\frac{1}{1 + (\frac{1}{x^{2}})} 脳 \frac{- 1}{x^{2}}}{\frac{- 1}{x^{2}}} = \lim_{x 鈫� 0} \frac{x^{2}}{1 + x^{2}} = \frac{0}{1 + 0} = 0$

Step 4. Graph Representation:

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Use the Squeeze Theorem to find each of the limits in Exercises. Explain exactly how the Squeeze Theorem applies in each case.
$\lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x}$

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Applying Squeeze theorem on the limit:

Step 3. Proving lim x→0x tan-11x=0

Step 4. Graph Representation:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

91影视

Use the Squeeze Theorem to find each of the limits in Exercises. Explain exactly how the Squeeze Theorem applies in each case.limx鈫�0xtan-11x

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Applying Squeeze theorem on the limit:

Step 3. Proving lim x→0x tan-11x=0

Step 4. Graph Representation:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Use the Squeeze Theorem to find each of the limits in Exercises. Explain exactly how the Squeeze Theorem applies in each case.
$\lim_{x 鈫� 0} x \tan^{- 1} \frac{1}{x}$