Q. 34 Evaluate the limits in Exercises... [FREE SOLUTION]

91影视

Chapter 12: Q. 34 (page 931)

Evaluate the limits in Exercises 33鈥�40 if they exist.
$\lim_{(x, y, z) 鈫� (3, - 4, 蟺 / 4)} \frac{x^{2} y^{}}{\tan z}$

Short Answer

Expert verified

The limit is $- 36$ .

Step by step solution

Given Information

Consider the function $\lim_{(x, y, z) 鈫� (3, - 4, 蟺 / 4)} \frac{x^{2} y^{}}{\tan z}$

The goal is to assess $\lim_{(x, y, z) 鈫� (3, - 4, 蟺 / 4)} \frac{x^{2} y^{}}{\tan z}$ $f$ if it exists.

Defining the limit

Consider the following assertion:

Consider a three-variable function $f (x, y, z)$ that is continuous at all points on $R^{3}$ . The limit of the function $f (x, y, z)$ as $(x, y, z) 鈫� (x_{0}, y_{0}, z_{0})$ is therefore defined as

$\lim_{(x, y, z) 鈫� (x_{0}, y_{0}, z_{0})} f (x, y, z) = f (x_{0}, y_{0}, z_{0})$

Evaluating the limit

Because $x^{2} y$ is a two-variable polynomial function, it is continuous for every point on $R^{3}$ , and the transcendental number $\tan z$ is also continuous for every point on $R^{3}$ .

Thus, where $\frac{x^{2} y}{\tan z}$ is continuous, where the rational function $\frac{x^{2} y}{\tan z}$ is defined .

As a result of the statement,

$\lim_{(x, y, z) 鈫� (3, - 4, 蟺 / 4)} \frac{x^{2} y^{}}{\tan z} = \frac{{(3)}^{2} (- 4)}{\tan 蟺 / 4} = - 36$

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

Evaluate the limits in Exercises 33鈥�40 if they exist.
$\lim_{(x, y, z) 鈫� (3, - 4, 蟺 / 4)} \frac{x^{2} y^{}}{\tan z}$

Short Answer

Step by step solution

Given Information

Defining the limit

Evaluating the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Decision Maths

Applied Mathematics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

Evaluate the limits in Exercises 33鈥�40 if they exist.lim(x,y,z)鈫�(3,-4,蟺/4)x2ytanz

Short Answer

Step by step solution

Given Information

Defining the limit

Evaluating the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Decision Maths

Applied Mathematics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Evaluate the limits in Exercises 33鈥�40 if they exist.
$\lim_{(x, y, z) 鈫� (3, - 4, 蟺 / 4)} \frac{x^{2} y^{}}{\tan z}$