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Find the value of k, if f(x) is continuous at x = 0: f(x) = (Sin3x/2)/x , x not equal to 0 k , x = 0

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f (x) = \frac{sin 3 x}{sin x}, x \neq 0

= K, x = 0

K =

f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{sin 3 x}{x^{2} + x}, & x \neq 0 λ + 2, & x = 0 \end{matrix}

is continuous at

x = 0,

then the value of

λ

Q. A continuous real function

f

f (2 x) = 3 f (x) \forall x \in R

1 \int 0 f (x) d x = 1

, then the value of definite integral

2 \int 1 f (x) d x

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{sin 3 x + a sin 2 x + b sin x}{x^{5}} & x \neq 0 c, & x = 0 \end{matrix}

is continuous at

x = 0

, find the values of

a, b, c

.

f : R \to R

be differentiable at

x = 0

f (0)

f^{'} (0) = 2

, then the value of

\begin{matrix} lim x \to 0 \end{matrix} \frac{1}{x} [f (x) + f (2 x) + f (3 x) + . . . + f (2015 x)]

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