`underset(h rarr 0)lim (sqrt(2x+3h)-sqrt(2x))/(2h)`, किसके बराबर है ?

Options

A. `(1)/(2sqrt(2x))`
B. `(3)/(sqrt(2x))`
C. `2(3)/(sqrt(2x))`
D. `(3)/(4sqrt(2x))`

Answer

D

Explanation

`underset(h rarr 0)lim(sqrt(2x+3h)-sqrt(2x))/(2h)`
L-Hospital से,
`=underset(hrarr0)lim((1)/(2sqrt(2x+3h)).3-0)/(2)`
`=underset(hrarr0)lim(3)/(4sqrt(2x+3h))`
`=(3)/(4).(1)/(sqrt(2x+0))=(3)/(4sqrt(2x))`