Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

Examine the following functions for continuity. $f(x) = \frac {1} { x - 5}, x \: \neq \: 5 $

$\begin{array}{1 1} \text{Yes, it is continuous} \\ \text{No, it is not continuous}\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 $\lim\limits_{x\to c} f(x) = f(c)$.
  • Sum, difference, product and quotient of any continuous functions is continous also.
Step 1:
$f(x)=\large\frac{1}{x-5}$
At $x=5$
$f(x)=\large\frac{1}{5-5}=\frac{1}{0}$
$\quad\quad\quad\quad\;\;\;=$Not defined.
Step 2:
When $x\neq 5\lim\limits_{\large x\to c}f(x)=\lim\limits_{\large x\to c}\large\frac{1}{x-5}=\frac{1}{c-5}$
$f(c)=\large\frac{1}{c-5}$
$f$ is continuous at $x\in R-\{5\}$
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.
...