Question

$\lim _{x\to \:0}\left(x\ln \left(x\right)\right)$

how to solve it ?????

Answer 1

$\lim _{x\to \:0}\left(x\ln \left(x\right)\right)=0$

Steps :-

$\mathrm{If\:}\lim _{x\to a-}f\left(x\right)=\lim _{x\to a+}f\left(x\right)=L\mathrm{\:then}\:\lim _{x\to a}f\left(x\right)=L$

$\lim _{x\to \:0-}\left(x\ln \left(x\right)\right)=0$

$\lim _{x\to \:0+}\left(x\ln \left(x\right)\right)=0$

$=0$

Answer 2

Answer:

The Laplace Convolution Theorem tells us that if we define the convolution of two function

f

(

t

)

and

g

(

t

)

by:

(

f

⋆

g

)

(

t

)

=

∫

t

0

f

(

t

−

x

)

g

(

x

)

d

x