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Let f and g be real valued functions def...

Let `f` and `g` be real valued functions defined on interval `(-1,\ 1)` such that `g"(x)` is continuous, `g(0)!=0` , `g'(0)=0,` `g"(0)!=0` , and `f(x)=g(x)sinx` . Statement-1 : `("Lim")_(x->0)[g(x)cotx-g(0)"c o s e c"x]=f"(0)` and Statement-2 : `f'(0)=g(0)`

A

Statement (1) is correct and statement (2) is correct and statement (2) is correct explanation for (1)

B

Statement (1) is correct and statement (2) is correct and statement (2) is NOT correct explanation for (1)

C

Statement (1) is true but (2) is false

D

Statement (1) is false but (2) is true

Text Solution

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The correct Answer is:
A
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