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What is lim(h to 0) (sqrt(2x+3h)-sqrt2x)...

What is `lim_(h to 0) (sqrt(2x+3h)-sqrt2x)/(2h)` equal to?

A

`(1)/(2sqrt2x)`

B

`(3)/(sqrt2x)`

C

`(3)/(2sqrt2x)`

D

`(3)/(4sqrt2x)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(hto0)lim(sqrt2x+3h-sqrt2x)/(2h)`
Rationalise the numerator.
`underset(hto0)lim((sqrt2x+3h-sqrt2x)/(2h)xx(sqrt2x+3h+sqrt2x)/(sqrt2x+3h+sqrt2x))`
`=underset(hto0)lim(2x+3h-2x)/(2h(sqrt2x+0+sqrt2))`
`=(3)/(2(sqrt2x+0+sqrt2x))=(3)/(4sqrt2x)`
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