Explanation Given Information: The function is, f ( x ) = { x 2 +1 if x ≤ 0 x if 0 < x < 1 2 x 2 − 1 if x ≥ 1 . Explanation: Consider the provided function, f ( x ) = { x 2 +1 if x ≤ 0 x if 0 < x < 1 2 x 2 − 1 if x ≥ 1 A function f ( x ) is continuous at x = c if the limit lim x → c f ( x ) exists. So, to check whether the function is continuous at x = 0 , consider the limit, lim x → 0 f ( x ) The lim x → c f ( x ) will exist at c if, lim x → c − f ( x ) = lim x → c + f ( x ) Now, the limit from the left is represented by lim x → 0 − f ( x ) and the limit from the right is represented by lim x → 0 + f ( x ) . The lim x → c f ( x ) will exist at c = 0 when the limit from the left, that is, the values of f ( c ) but c < 0 , is equal to the limit from the right, that is, the values of f ( c ) but c > 0

12th Edition

ISBN: 9780840058225

Author: HARSHBARGER

Publisher: CENGAGE L

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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 topic…

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Chapter 9, Problem 28RE

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Whether the function, f(x)={x2+1 if x≤0x if 0<x<12x2−1 if x≥1 is continuous at x=0.

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Chapter 9, Problem 27RE

Chapter 9, Problem 29RE

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Ch. 9.1 - 1. Can exist if is undefined? Ch. 9.1 - 2. Does exist if ? Ch. 9.1 - 3. Does Ch. 9.1 - 4. If , does exist? Ch. 9.1 - 5. Let (a) Does (b) Find . Ch. 9.1 - 6. Evaluate the following limits (if they...Ch. 9.1 - Prob. 7CP Ch. 9.1 - Prob. 8CP Ch. 9.1 - Prob. 9CP Ch. 9.1 - Prob. 10CP

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Whether the function, f ( x ) = { x 2 +1 if x ≤ 0 x if 0 < x < 1 2 x 2 − 1 if x ≥ 1 is continuous at x = 0 .

Solution Summary: The author explains that the function is continuous at x=c if the limit undersetxto cmathrmlim

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Whether the function, f(x)={x2+1 if x≤0x if 0<x<12x2−1 if x≥1 is continuous at x=0.

Want to see the full answer?

Chapter 9 Solutions

Whether the function, f ( x ) = { x 2 +1 if x ≤ 0 x if 0 &lt; x &lt; 1 2 x 2 − 1 if x ≥ 1 is continuous at x = 0 .

Solution Summary: The author explains that the function is continuous at x=c if the limit undersetxto cmathrmlim

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Whether the function, f(x)={x2+1 if x≤0x if 0<x<12x2−1 if x≥1 is continuous at x=0.

Want to see the full answer?

Chapter 9 Solutions

Whether the function, f ( x ) = { x 2 +1 if x ≤ 0 x if 0 < x < 1 2 x 2 − 1 if x ≥ 1 is continuous at x = 0 .