The value of lim x → 0 x 6 c o s ( s i n 2 x ) − c o s ( x 2 ) is

lim x → 0 x 6 c o s ( s i n 2 x ) − c o s ( x 2 ) = lim x → 0 x 6 2 s i n ( 2 s i n 2 x + x 2 ) ⋅ s i n ( 2 x 2 − s i n 2 x )

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Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsTrigonometric and Inverse Trigonometric limitsMedium2 minQB

MathematicsMediumsingle choice

The value of $lim_{x \to 0} \frac{c o s ( s i n ^{2} x ) - c o s ( x ^{2} )}{x ^{6}}$ is

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Answer:

Solution:

$lim_{x \to 0} \frac{c o s ( s i n ^{2} x ) - c o s ( x ^{2} )}{x ^{6}}$ $= lim_{x \to 0} \frac{2 s i n ( \frac{s i n ^{2} x + x ^{2}}{2} ) \cdot s i n ( \frac{x ^{2} - s i n ^{2} x}{2} )}{x ^{6}}$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Trigonometric and Inverse Trigonometric limits

⏱ 2mℹ️ Source: QB

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