Question

Hello! Help me solve this please : lim x→1 (1/x - 1)/(x-1). The answer is -1. I'd like to know the working. :(

Answer 1

\[\lim\limits_{ x→1 }\left(\frac{\frac 1{x}-1}{x-1}\right)\]
?

Answer 2

or\[\lim\limits_{ x→1 }\left(\frac{\frac 1{x-1}}{x-1}\right)\]
?

Answer 3

UNCLERHAUKUS, the first one that you posted.

Answer 4

are you familiar wit L'hopital rule ??

Answer 5

@sami-21 I've learned that (L'hospital rule) in college but I hardly understand it. Lol. Is it easier?

Answer 6

@UnkleRhaukus Yeahhh the first one that you posted. (I couldn't copy the equation.)

Answer 7

I think it is very simple...

Answer 8

@waterineyes Help me please. I suck at Calculus :|

Answer 9

it is Just take derivative of numerator and denominator then apply the limits.
\[\Large \frac{\frac{d}{dx}(\frac{1}{x}-1)}{\frac{d}{dx}(x-1)}\]
after taking derivative we are left with
\[\Large \frac{-1}{x^2}\] (deliminator gets one )
now apply the limits
\[\Large \lim_{x \rightarrow 1}(\frac{-1}{x^2})=\frac{-1}{1}=-1\]
i hope it is clear

Answer 10

@eyka94 is it ok now ?

Answer 11

\[\lim\limits_{ x→1 }\left(\frac{\frac 1{x}-1}{x-1}\right) \implies \lim_{x \rightarrow 1}(\frac{1-x}{x(x-1)}) \implies (-1)\lim_{x \rightarrow 1}\frac{x-1}{x(x-1)}\]

\[\implies (-1) \lim_{x \rightarrow 1}\frac{1}{x}\]

Plug in the limits now..

Answer 12

@sami-21 Thank you. But this question is under "Limits and Continuity" chapter. Can we answer it in a "LIMIT" way. :P

Answer 13

There is no need of derivative..

Answer 14

yes you can do it.

Answer 15

@waterineyes @sami-21 Thanks to you both! <3 Well it's my first day here and barely know anything about how to use this website haha. Thanks again. ;)

Answer 16

Welcome dear..

Answer 17

you 're welcome :)

Answer 18

\[\huge \color{blue}{\textbf{Welcome To Openstudy..}}\]

Answer 19

THANK I LOVE YOU ALL!