Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

If $f(x)=(x+1)^{\cot x}$ is continuous at $x=0$ then $f(0)$ is

$(a)\;0\qquad(b)\;\large\frac{1}{e}$$\qquad(c)\;e\qquad(d)\;None\;of\;these$

2 Answers

Comment
A)
$\lim\limits_{x\to 0}f(x)=\lim\limits_{x\to 0}(1+x)^{\Large\frac{1}{x}.\normalsize x\cot x}$
$\Rightarrow e^{\large\lim\limits_{x\to 0}x\cot x}$
$\Rightarrow e^{\large\lim\limits_{x\to 0}x\Large\frac{x}{\tan x}}$
$\Rightarrow e^1$
$\Rightarrow e$
Since $f(x)$ is continuous at $x=0$
$f(0)=e$
Hence (c) is the correct answer.
 
Comment
A)
'e' is the answer.
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.
...