Chapter 1: Q. 17 (page 135)

Suppose f and g are functions such that $\lim_{x \to 3} f (x) = 5, \lim_{x \to 4} f (x) = 2$ and $\lim_{x \to 3} g (x) = 4$
Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.
$\lim_{x \to 3} \frac{f (x) - 3}{g (x)}$

Short Answer

Expert verified

The value of $\lim_{x \to 3} \frac{f (x) - 3}{g (x)} = \frac{1}{2}$

Step by step solution

Step 1. Given information

The given limit $\lim_{x \to 3} \frac{f (x) - 3}{g (x)}$ and the given values are, $\lim_{x \to 3} f (x) = 5, \lim_{x \to 4} f (x) = 2$ and $\lim_{x \to 3} g (x) = 4$

Step 2. Calculating value of the given limits

The value can be calculated as below,

$\lim_{x \to 3} \frac{f (x) - 3}{g (x)} = \frac{\lim_{x \to 3} f (x) - 3}{\lim_{x \to 3} g (x)} [q u o t i e n t r u l e] = \frac{\lim_{x \to 3} f (x) - \lim_{x \to 3} 3}{\lim_{x \to 3} g (x)} [s u m r u l e] = \frac{5 - 3}{4} = \frac{2}{4} = \frac{1}{2}$

Hence,the result is $\frac{1}{2}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Suppose f and g are functions such that $\lim_{x \to 3} f (x) = 5, \lim_{x \to 4} f (x) = 2$ and $\lim_{x \to 3} g (x) = 4$
Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.
$\lim_{x \to 3} \frac{f (x) - 3}{g (x)}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating value of the given limits

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Suppose f and g are functions such thatlimx→3f(x)=5,limx→4f(x)=2 andlimx→3g(x)=4Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.limx→3f(x)-3g(x)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating value of the given limits

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Suppose f and g are functions such that $\lim_{x \to 3} f (x) = 5, \lim_{x \to 4} f (x) = 2$ and $\lim_{x \to 3} g (x) = 4$
Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.
$\lim_{x \to 3} \frac{f (x) - 3}{g (x)}$