Chapter 14: Q. 45 (page 889)

In Problems 45-60, determine whether $f$ is continuous at $c$ .
$f (x) = x^{3} - 3 x^{2} + 2 x - 6, c = 2$

Short Answer

Expert verified

The function is continuous at $c$

Step by step solution

Given information

Given function

$f (x) = x^{3} - 3 x^{2} + 2 x - 6 c = 2$

Check whether the function is defined at c

Checking, we get

$f (2) = 2^{3} - 3 (2)^{2} + 2 (2) - 6 f (2) = 8 - 3 (4) + 2 (2) - 6 f (2) = 8 - 12 + 4 - 6 f (2) = - 6$

So it is defined at $c$

Check the left hand limits and right hand limits

We have,

$\lim_{x \to 2^{-}} f (x) = 2^{3} - 3 (2)^{2} + 2 (2) - 6 \lim_{x \to 2^{-}} f (x) = 8 - 3 (4) + 2 (2) - 6 = - 6$

Again,

$\lim_{x \to 2^{+}} f (x) = \lim_{x \to 2^{+}} 2^{3} - 3 (2)^{2} + 2 (2) - 6 \lim_{x \to 2^{+}} f (x) = \lim_{x \to 2^{+}} 8 - 3 (4) + 2 (2) - 6 \lim_{x \to 2^{+}} f (x) = - 6$

Since $\lim_{x \to c} f (x) = f (c)$ so it is continuous at $c$

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In Problems 45-60, determine whether $f$ is continuous at $c$ .
$f (x) = x^{3} - 3 x^{2} + 2 x - 6, c = 2$

Short Answer

Step by step solution

Given information

Check whether the function is defined at c

Check the left hand limits and right hand limits

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In Problems 45-60, determine whether fis continuous at c.f(x)=x3-3x2+2x-6,c=2

Short Answer

Step by step solution

Given information

Check whether the function is defined at c

Check the left hand limits and right hand limits

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Geometry

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 45-60, determine whether $f$ is continuous at $c$ .
$f (x) = x^{3} - 3 x^{2} + 2 x - 6, c = 2$