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  • a)
    g'(0) = – cos(log2)
  • b)
    g is differentiable at x = 0 and g'(0) = – sin(log2)
  • c)
    g is not differentiable at x = 0
  • d)
    g'(0) = cos(log2)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
a)g(0) = – cos(log2)b)g is differentiable at x = 0 and g(0) = &n...
g (x) = f (f (x))
In the neighbourhood of x = 0,
(x) =  | log2 – sin x| = (log 2 – sin x)
∴ g (x) = |log 2 – sin| log 2 – sin x || = (log 2 – sin(log 2 – sin x))
∴ g (x) is differentiable and g'(x) = – cos(log 2 – sin x) (– cos x)
⇒ g'(0) = cos (log 2)
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a)g(0) = – cos(log2)b)g is differentiable at x = 0 and g(0) = – sin(log2)c)g is not differentiable at x = 0d)g(0) = cos(log2)Correct answer is option 'D'. Can you explain this answer?
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