The value of f(0) for whichf(x)=64x+4-2sin 2x is continuous

f0=limx→0fx⇒ limx→06412x+42 cos 2x=8 ∴f0=8

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The value of f(0) for which
$f (x) = \frac{64 (\sqrt{x + 4} - 2)}{\sin 2 x} is continuous$

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answer is 8.

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$f (0) = \lim_{x \to 0} \underset{}{f (x) \Rightarrow} \lim_{x \to 0} \frac{64 [\frac{1}{2 \sqrt{x + 4}}]}{2 \cos 2 x} = 8 ∴ f (0) = 8$

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