11Is the answer (c) ?????
If f(0)=f(1)=12,|f'(1)|<1 and f'(0)=2,then
\lim_{x\rightarrow 0} \frac{f(sin x)-f(cos x)}{x} is
A. 0 B. 1
C. 2 D. 1/2
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5 Answers
11Since it is indeterminate form, we can simply use L - Hospital's rule,
see clearly, it is given that f(0) = f(1) , therefore, it is 0 / 0 form and use L'H rule
lim x→0 cosx f ' (sin x ) + f'(cosx) sinx
= f ' (sin 0 ) = f ' (0) = 2
1zero by zero form.
applying l-hospitals rule
L=(f'(sin(x))cos(x)+f'(cos(x))sin(x))/1
putting x=0
L comes out to be 2.