The function f(x) = sin(6 x) / x is not defined at 0. Decide how to define f(0) so that f(x) is...
Question:
The function {eq}f(x) = \frac{\sin(6 x)}x {/eq} is not defined at 0. Decide how to define f(0) so that f(x) is continuous at 0.
Continuity of a Function:
The function is continuous at a point {eq}x=a {/eq} if it satisfies the following condition:
{eq}\lim_{x\rightarrow a}f(x)=f(a) {/eq}
i.e. the limit as {eq}x {/eq} tends to {eq}a {/eq} should be equal to the value of the function at {eq}x=a. {/eq}
A function which is not continuous at a point in the domain of the function is called a discontinuous function.
Some discontinuous functions can have removable discontinuity. That means we can remove the discontinuity by redefining the given function at the point of discontinuity.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answer
The given function is:
{eq}f(x) = \frac{\sin(6 x)}{x} {/eq}
The limit of the function at {eq}x=0 {/eq} is:
{eq}\\\\\begin{align*}...
See full answer below.
Learn more about this topic:
from
Chapter 5 / Lesson 6Learn to define what a removable discontinuity is. Discover the removable discontinuity graph and limit. Learn how to find a removable discontinuity. See examples.