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lim ( x to 0 ) (( 3^ x - 1 ) /( ...

` lim _ ( x to 0 ) (( 3^ x - 1 ) /( x )) ` is equal to

A

` 2 log 3 `

B

`3log 3 `

C

` log 3 `

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
` lim _ ( xto 0 ) (( 3^ x - 1 ) / ( x ))" " ( ( 0) /( 0) ` form )
Using L' Hospital's rule,
`= lim _ ( x to 0 ) ( 3 ^ x log 3 - 0 ) /( 1 ) = 3^ 0 log 3 `
` = log 3 `
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