displaystyle limx → π/6 (2 sin2 x+sin x-1/2 sin2 x-3 sin x+1)

Question

displaystyle limx → π/6 (2 sin2 x+sin x-1/2 sin2 x-3 sin x+1) (A) 3 (B) -3 (C) 6 (D) 0

Tardigrade Admin · Accepted Answer

We have, displaystyle limx → (π/6) (2 sin2 x+sin x-1/2 sin2 x-3 sin x+1) ( (0/0) form) = displaystyle limx → (π/6)((sin x+1)(2 sin x-1)/(sin x-1)(2 sin x-1)) = displaystyle limx → (π/6)((sin x+1)/(sin x-1)) =( displaystyle limx → π/6(sin x+1)/ displaystyle limx → π/6(sin x-1)) =(((1/2)+1)/((1)2-1))=-3

Q. $x \to π /6 lim$ $\frac{2 s i n ^{2} x + s in x - 1}{2 s i n ^{2} x - 3 s in x + 1}$

$3$

$- 3$

$6$

$0$

Q. x→π/6lim​ 2sin2x−3sinx+12sin2x+sinx−1​

3

−3

6

0

We have, x→6π​lim​ 2sin2x−3sinx+12sin2x+sinx−1​ (00​ form) =x→6π​lim​(sinx−1)(2sinx−1)(sinx+1)(2sinx−1)​ =x→6π​lim​(sinx−1)(sinx+1)​ =x→π/6lim​(sinx−1)x→π/6lim​(sinx+1)​ =(21​−1)(21​+1)​=−3

Q. $x \to π /6 lim$ $\frac{2 s i n ^{2} x + s in x - 1}{2 s i n ^{2} x - 3 s in x + 1}$

$3$

$- 3$

$6$

$0$