` lim _ (x to 0) ( e^(x) - e^(-x))/x ` का मान ज्ञात कीजिए ।

Options

A. `2`
B. `5`
C. `7`
D. `3`

Answer

A

Explanation

` lim_( h to 0) ( e^(x) -e^(x))/x = lim _( x to 0) 1/x [( 1+ x+ x^(2)/(2!) + x^(3)/(3!) + . . . . ) - [( 1- x+ x^(2)/(2!)- x^(3)/(3 !) + ....)]`
` = lim_( x to 0) 1/x [ 2 ( x- x^(3) /(3!) [ 2 ( x - x^(3)/(3!)+ ......)]`
` = lim_( x to 0) [ 2 ( 1+ x^(2)/(3!) + ......)]" " [ :' x !=0]`
`=2`.