Q. 84 Use what you know about one-side... [FREE SOLUTION]

Chapter 1: Q. 84 (page 122)

Use what you know about one-sided limits to prove that a function $f$ is continuous at a point $x = c$ if and only if it is both left and right continuous at $x = c$ .

Short Answer

Expert verified

Ans: If LHL (Left Hand Limit) =RHL(Right Hand Limit) At point $x = c$ then, function $f$ is continuous at a point $x = c$ .

Step by step solution

Step 1. Given information.

given, both left and right continuous at $x = c$

Step 2. Find LHL and RHL at point x=c.

Finding limits at point $x = c$

LHL role="math" localid="1648012913505" $= lim_{x 鈫� c^{鈭�}} 鈥� f (x) = c$

RHL role="math" localid="1648012924655" $= lim_{x 鈫� c^{+}} 鈥� f (x) = c$

Step 3. Proof.

Since, LHL =RHL

Then, we can say that $f$ is continuous at a point $x = c$ .

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91影视

Use what you know about one-sided limits to prove that a function $f$ is continuous at a point $x = c$ if and only if it is both left and right continuous at $x = c$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find LHL and RHL at point x=c.

Step 3. Proof.

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91影视

Use what you know about one-sided limits to prove that a function f is continuous at a point x=cif and only if it is both left and right continuous at x=c.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find LHL and RHL at point x=c.

Step 3. Proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

Use what you know about one-sided limits to prove that a function $f$ is continuous at a point $x = c$ if and only if it is both left and right continuous at $x = c$ .