Question

Evaluate the given question
​

Answer 1

The limit does not exist

Answer 2

Solution given:

`Lim_(h\rightarrow) (√(x+h)-√(x))/(h)`

The given expression takes the form of
`(0)/(0)`

when h=0

now

`lim_(h\rightarrow 0) (√(x+h)-√(x))/(h)*(√(x+h)+√(x))/(√(x+h)+√(x))`

`lim_(h\rightarrow 0)\frac{(x+h)-x}{h*({√(x+h)+√(x)})}`

`lim_(h\rightarrow 0)\frac{h}{h*({√(x+h)+√(x)})}`

`lim_(h\rightarrow 0)\frac{1}{({√(x+h)+√(x)})}`

=
`(1)/(√(x+0)+√(x))`

=
`(1)/(2√(x))`