Answered: Activity 2 1. Show that g(x) = x² + 1…

Activity 2 1. Show that g(x) = x² + 1 is continuous at x = 1. a. g(x) b. lim g(x) X-1 c. Is the limit equal to the function value? Conclusion: Is the function continuous at x = 1?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Activity 2
1. Show that g(x) = x² + 1 is continuous at x = 1.
a. g(x)
b. lim g(x)
X-1
c. Is the limit equal to the function value?
Conclusion:
Is the function continuous at x = 1?

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