Question

show that lim x --> 0 (1/x) does not exist...

please I need the answer

Answer 1

Step-by-step explanation:

0 × anything we will get 0

so that 0(1/x) value is 0

so x doesn't not exist in 0

Answer 2

Answer:

$\bf\underbrace\orange{Answer:}$

Concept used :-

We have to evaluate Left Hand Limit and then Right Hand Limit,

if on evaluation, LHL = RHL, then Limit exist otherwise Limit doesnot exist.

$\bf\underbrace\orange{Solution:}$

$\bf \:f(x) = \dfrac{1}{x} \: at \: x \: = 0$

Evaluation of LHL :-

$\bf \:\lim_{x\rightarrow 0^ - } \frac{1}{x}$

Put x = 0 - h, i.e. x = - h,

where h --> 0 as x --> 0.

$\bf \:\lim_{h\rightarrow 0} \frac{1}{ - h} = - \infty$

Evaluation of RHL :-

$\bf \:\lim_{x\rightarrow 0^+} \dfrac{1}{x}$

Put x = 0 + h, i.e. x = h,

where h --> 0 as x --> 0.

$\bf \:\lim_{h\rightarrow 0} \frac{1}{h} = \infty$

Since, LHL = RHL

⇛ Limit doesnot exist.

_____________________________________________