X - 0lim -1-cos2x-2x isJEE 2002

X → 0lim√(1 cos2x)/√(2)x = x → 0lim√(1 (1 2sin^2x))/√(2)x; x → 0lim√(2 sin^2 x)/√(2)x = x → 0lim|sin x|/x The limit of above does not exist as LHS = 1 ≠ RHL ...

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Standard XIII

Mathematics

Existence of Limit

x → 0lim √1-c...

Question

$lim x \to 0 \frac{\sqrt{1 - c o s 2 x}}{\sqrt{2} x}$ is

(JEE 2002)

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-1

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Zero

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Does not exist

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Solution

The correct option is D
Does not exist

$lim x \to 0 \frac{\sqrt{1 - c o s 2 x}}{\sqrt{2} x} = lim x \to 0 \frac{\sqrt{1 - (1 - 2 s i n^{2} x})}{\sqrt{2} x};$
$lim x \to 0 \frac{\sqrt{2 s i n^{2} x}}{\sqrt{2} x} = lim x \to 0 \frac{| s i n x |}{x}$

The limit of above does not exist as LHS = -1 $\neq$ RHL = 1

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limx→0 √1−cos2x√2x is (JEE 2002)

The correct option is D Does not exist limx→0√1−cos2x√2x=limx→0√1−(1−2sin2x)√2x; limx→0√2sin2x√2x=limx→0|sin x|x The limit of above does not exist as LHS = -1 ≠ RHL = 1

$lim x \to 0 \frac{\sqrt{1 - c o s 2 x}}{\sqrt{2} x}$ is

(JEE 2002)