Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

Examine the continuity of the function $f (x) = 2x^2 - 1$ at $x = 3$

$\begin{array}{1 1}\text{f(x) is continuous at x=3} \\ \text{f(x) is NOT continuous at x=3} \end{array} $

1 Answer

Comment
A)
Toolbox:
  • If $f$ is a real function on a subset of the real numbers and $c$ a point in the domain of $f$, then $f$ is continous at $c$ if $\lim\limits_{x\to c} f(x) = f(c)$.
Given $f(x) = 2x^2-1$.
At $x=3, \; \lim\limits_{x\to 3} f(x) = \lim\limits_{x\to 3} 2x^2-1 = 2 \times 3^2 -1 = 2 \times 9 - 1= 18-1 = 17$
$f(3) = 2 \times 3^2 -1 = 2 \times 9 - 1= 18-1 = 17$
Since $\lim\limits_{x\to 3} f(x) = f(3), f(x)$ is continous at $x=3$.
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...