Q. 7 what it means, in terms of limit... [FREE SOLUTION]

Chapter 1: Q. 7 (page 152)

what it means, in terms of limits, for a function f to be continuous at a point $x = c$ , left continuous at $x = c$ , and right continuous at $x = c .$

Short Answer

Expert verified

If limit $\lim_{x 鈫� c} f (x) = f (c),$ then function f is continuous at $x = c .$

If left limit $\lim_{x 鈫� c^{-}} f (x) = f (c),$ then function f is left continuous at $x = c .$

If Right limit role="math" localid="1648278049295" $\lim_{x 鈫� c^{+}} f (x) = f (c),$ then function f is right continuous at $x = c .$

Step by step solution

Step 1. Given information.

A function f is continuous at $x = c .$

function f is left continuous at $x = c .$

functionf is right continuous at $x = c .$

Step 2. continuous function

A function is continuous at $x = c$ if its limit as $x 鈫� c$ is equal to the function value at $x = c .$

$\lim_{x 鈫� c} f (x) = f (c)$

Step 3. Left continuous function

A function is left continuous at $x = c$ if its left limit as $x 鈫� c^{-}$ is equal to the function value at $x = c$ .

$\lim_{x 鈫� c^{-}} f (x) = f (c)$

Step 4. Right continuous function

A function is right continuous at $x = c$ if its right limit as $x 鈫� c^{-}$ is equal to the function value at $x = c .$

$\lim_{x 鈫� c^{+}} f (x) = f (c)$

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91影视

what it means, in terms of limits, for a function f to be continuous at a point $x = c$ , left continuous at $x = c$ , and right continuous at $x = c .$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. continuous function

Step 3. Left continuous function

Step 4. Right continuous function

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91影视

what it means, in terms of limits, for a function f to be continuous at a pointx=c, left continuous atx=c, and right continuous atx=c.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. continuous function

Step 3. Left continuous function

Step 4. Right continuous function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Statistics

Calculus

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

what it means, in terms of limits, for a function f to be continuous at a point $x = c$ , left continuous at $x = c$ , and right continuous at $x = c .$