displaystyle limx → 0 (1 - cos 2x/x2) is

Question

displaystyle limx → 0 (1 - cos 2x/x2) is (A) (-1/2) (B) (1/2) (C) 2 (D) -2

Tardigrade Admin · Accepted Answer

displaystyle limx → 0 (1 - cos 2x/x2) = displaystyle limx → 0 (2 sin2 x/x2) = 2 displaystyle limx → 0 (( sin x/x) . ( sin x/x) ) = 2 displaystyle limx → 0 ( sin x/x) . displaystyle limx → 0 ( sin x/x) = 2 (1) (1) = 2

Q. $x \to 0 lim \frac{1 - cos 2 x}{x ^{2}}$ is

$\frac{- 1}{2}$

$\frac{1}{2}$

2

-2

$x \to 0 lim \frac{1 - cos 2 x}{x ^{2}} = x \to 0 lim \frac{2 sin ^{2} x}{x ^{2}}$
$= 2 x \to 0 lim (\frac{sin x}{x} . \frac{sin x}{x})$
$= 2 x \to 0 lim \frac{sin x}{x} . x \to 0 lim \frac{sin x}{x} = 2 (1) (1) = 2$

Q. x→0lim​x21−cos2x​ is

2−1​

21​

2

-2

x→0lim​x21−cos2x​=x→0lim​x22sin2x​ =2x→0lim​(xsinx​.xsinx​) =2x→0lim​xsinx​.x→0lim​xsinx​=2(1)(1)=2

Q. $x \to 0 lim \frac{1 - cos 2 x}{x ^{2}}$ is

$\frac{- 1}{2}$

$\frac{1}{2}$

$x \to 0 lim \frac{1 - cos 2 x}{x ^{2}} = x \to 0 lim \frac{2 sin ^{2} x}{x ^{2}}$
$= 2 x \to 0 lim (\frac{sin x}{x} . \frac{sin x}{x})$
$= 2 x \to 0 lim \frac{sin x}{x} . x \to 0 lim \frac{sin x}{x} = 2 (1) (1) = 2$