Chapter 14: Q. 12 (page 905)

In Problem, determine whether f is continuous at c.
$f (x) = 3 x^{4} - x^{2} + 2, c = 5$

Short Answer

Expert verified

The given polynomial function is $f (x) = 3 x^{4} - x^{2} + 2$ continuous at c = 5

Step by step solution

Step1. Given information

Polynomial function $f (x) = 3 x^{4} - x^{2} + 2$

c=5

We know that

A function is called continuous function when at x= a,

localid="1647106984859" $\underset{x \to a}{l i m} f (x) = f (a)$

and defined for every number of domain

Step2. Calculations of continuity

$\underset{x \to 5}{l i m} f (x) = f (5) = 3 {(5)}^{4} - {(5)}^{2} + 2 = 1875 - 25 + 2 = 1852$

as $\underset{x \to 5}{l i m} f (x) = f (5)$

so the polynomial function is continuous at c= 5

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In Problem, determine whether f is continuous at c.
$f (x) = 3 x^{4} - x^{2} + 2, c = 5$

Short Answer

Step by step solution

Step1. Given information

Step2. Calculations of continuity

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In Problem, determine whether f is continuous at c.
$f (x) = 3 x^{4} - x^{2} + 2, c = 5$