The function `f(x)={((sin3x)/x ,x!=0),(k/2,x=0):}` is continuous of `x=0,t h e nk=` (a) 3 (b) 6 (d) 9 (d) 12

Explanation

`f(0)=frac{k}{2}`


`f(x)=frac{sin 3 x}{x} quad x=0`


`lim _{x -> 0} frac{sin 3 x}{x} quad {lin} frac{sin f(x)}{f(x)}=1`


`f(x)=0`


`lim _{x -> 0^{-}} frac{sin (3 x)}{3 x} times 3 Rightarrow 3`


`lim _{x -> 0^{+}} quad frac{sin 3 x}{3 x} 3 Rightarrow 3`


LH.S `3=` RHS `=text { continue } f(0)`


`3=3=k / 2`


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