`("lim")_(xvec0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)=` `-1` (b) 1 (c) 0 (d) 2

Options

A. 2
B. 1
C. `log_(a)2`
D. 0

Answer

B

Explanation

`underset(xto0)lim(log(1+x+x^(2))+log(1-x+x^(2)))/(secx-cosx)`
`=underset(xto0)lim(log["("1+x^(2)")"^(2)-x^(2)])/((1-cos^(2)x)//cosx)`
`=underset(xto0)lim(log(1+x^(2)+x^(4)))/(sinxtanx)`
`=underset(xto0)lim(log(1+x^(2)(1+x^(2))))/(x^(2)(1+x^(2))).x^(2)(1+x^(2)).(1)/((sinx)/(x).(tanx)/(x).x^(2))`
`=1" "(" as "underset(xto0)lim(log(1+x))/(x)=1)`