undersetx→ (π /6) mathop lim ( sin 2x/ sin x) is equal to

Question

undersetx→ (π /6) mathop lim ( sin 2x/ sin x) is equal to (A)  √3  (B)  (1/√3)  (C)  2  (D)  (1/2)

Tardigrade Admin · Accepted Answer

lim x arrow (π/6) ( sin 2 x/ sin x)= lim x arrow (π/6) (2 sin x cos x/ sin x)=2 lim cos x=2 (√3/2)=√3 Alternate Method: lim x arrow (π/6) ( sin 2 x/ sin x)=( sin 2 (π/6)/ sin (π)6)=(√3 / 2/1 / 2)=√3

Q. $x \to \frac{π}{6} lim \frac{s i n 2 x}{s i n x}$ is equal to

$3$

$\frac{1}{3}$

$2$

$\frac{1}{2}$

$lim_{x \to \frac{π}{6}} \frac{s i n 2 x}{s i n x} = lim_{x \to \frac{π}{6}} \frac{2 s i n x c o s x}{s i n x} = 2 lim cos x = 2 \frac{3}{2} = 3$
Alternate Method: $lim_{x \to \frac{π}{6}} \frac{s i n 2 x}{s i n x} = \frac{s i n 2 \frac{π}{6}}{s i n \frac{π}{6}} = \frac{3 /2}{1/2} = 3$

Q. x→6π​lim​sinxsin2x​ is equal to

3​

3​1​

2

21​

limx→6π​​sinxsin2x​=limx→6π​​sinx2sinxcosx​=2limcosx=223​​=3​ Alternate Method: limx→6π​​sinxsin2x​=sin6π​sin26π​​=1/23​/2​=3​

Q. $x \to \frac{π}{6} lim \frac{s i n 2 x}{s i n x}$ is equal to

$3$

$\frac{1}{3}$

$2$

$\frac{1}{2}$

$lim_{x \to \frac{π}{6}} \frac{s i n 2 x}{s i n x} = lim_{x \to \frac{π}{6}} \frac{2 s i n x c o s x}{s i n x} = 2 lim cos x = 2 \frac{3}{2} = 3$
Alternate Method: $lim_{x \to \frac{π}{6}} \frac{s i n 2 x}{s i n x} = \frac{s i n 2 \frac{π}{6}}{s i n \frac{π}{6}} = \frac{3 /2}{1/2} = 3$