` lim_( x to 0) ( e^(x) - 1)/x ` का मान ज्ञात कीजिए ।

Options

A. `3`
B. `5`
C. `7`
D. `1`

Answer

D

Explanation

` lim _ ( x to 0) ( e^(x) - 1)/x = lim_( x to 0) (( 1+ x+ x^(2)/(2!) + x^(3)/(3!) + ......oo)-1)/x`
` = lim _( x to 0) (( x+ x^(2)/2 + x^(3)/(3!) + . . . . .oo))/x`
` = lim _ ( x to 0) (x(1+x/(2!) + x^(2)/(3!) + . . . . . oo))/x`
` -lim _ ( x to 0) (x(1+x/(2) + x^(2)/(3!) + . . . . . oo))/x" " ( जब x != 0)`
`=1.`