` lim _( x to 0) (sqrt(1+x)-sqrt(1-x))/x=......`

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

A

Explanation

बायां पक्ष
` lim _( x to 0) (sqrt(1+x)-sqrt(1-x))/x`
अंश और हर में ` ( sqrt( 1+x) + sqrt(1-x))` से गुणा करने पर
` = lim _( x to 0) ((sqrt(1+x)-sqrt(1-x))(sqrt(1+x)+ sqrt( 1-x)))/(x(sqrt(1+x)+sqrt(1-x)))`
` = lim _(x to 0 ) ((1+x) - (1 -x))/((sqrt(1+x)+sqrt(1-x)))`
`= lim _( x to 0)(1+x-1+x)/(x(sqrt(1+x) +sqrt(1-x)))`
` = lim _( x to 0) ( 2x)/( x (sqrt(1+x)+sqrt(1+x)))`
` = lim _( x to 0) 2/(sqrt(1+x)+ sqrt(1+x))`
` = 2/( (sqrt(1+0)+ sqrt (1-0)))`
` = 2/( 1+1)`
` = 2/2 = 1 `
= दाया पक्ष ।