` lim _( x to 1) (x^(15)-1)/(x^(10)-1)` का मान ज्ञात कीजिए ।

Options

A. `0`
B. `1/2`
C. `1`
D. `3/2`

Answer

D

Explanation

` lim_( x to1) (x^(15)-1)/(x^(10)-1)= lim _( x to 1) [ (x^(15)-1)/(x -1)div(x^(10)-1)/( x-1)]`
` = lim _( x to 1 ) ((x^(15)-1)/(x-1)) div lim _( x to 1 ) ((x^(10) - 1 )/(x-1))`
` = 15 ( 1)^(15-1) div 10 (1)^(10-1) [ :' lim _( x to 1 ) (x^(n)-a^(n))/(x-a) = nx^(n-1)` के प्रयोग से ]
` = 15(1) ^(14) div 10(1)^(9) `
`= 15 div 10`
` = 15/10 = 3/2`