Chapter 1: Q. 65 (page 88)

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.
$\lim_{x \to 1} f (x), f o r f (x) = \{\begin{cases} x^{2} + 1, i f x < 1 \\ 3, i f x = 1 \\ 3 - x, i f x > 1 \end{cases}$

Short Answer

Expert verified

The graph for the given limit

The limit expression does not have any value

Step by step solution

Step 1. Given information

The given limit $\lim_{x \to 1} f (x), f o r f (x) = \{\begin{cases} x^{2} + 1, i f x < 1 \\ 3, i f x = 1 \\ 3 - x, i f x > 1 \end{cases}$

Step 2. Sketch graphs by hand and use them to make approximations for the limit

The graph is drawn as below:

From the graph,we see that for the left of $x \to 1$ the value of the function is 2,Again for the right of $x \to 1$ the value is 2

Therefore the limit expression does not have any value

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.

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.
$\lim_{x \to 1} f (x), f o r f (x) = \{\begin{cases} x^{2} + 1, i f x < 1 \\ 3, i f x = 1 \\ 3 - x, i f x > 1 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Sketch graphs by hand and use them to make approximations for the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Applied Mathematics

Geometry

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.limx→1f(x),forf(x)=x2+1,ifx<13,ifx=13-x,ifx>1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Sketch graphs by hand and use them to make approximations for the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Applied Mathematics

Geometry

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.
$\lim_{x \to 1} f (x), f o r f (x) = \{\begin{cases} x^{2} + 1, i f x < 1 \\ 3, i f x = 1 \\ 3 - x, i f x > 1 \end{cases}$