(a) `lim_( x to 0 ) (3sqrt(1+x)-1)/x` का मान ज्ञात कीजिए ।

Options

A. `1/2`
B. `1/3`
C. `2`
D. `3`

Answer

B

Explanation

` lim _( x to 0 ) ( 3sqrt(1+ x) -1)/x = lim _( x to 0 ) (( 1+ 3) ^(1/3) - 1 )/x `
` = lim _ ( x to 0 ) (1+ 1/3x+ (1/3(1/3-1))/(2!) x^(2) + . . . . .oo -1 )/x`
` = lim _( x to 0 ) 1/3 + ( 1/3 (-2/3 )x)/(2!) + . . . . . oo`
` = 1/3 + 0 = 1/3 `