The function `f(x)={(sin3x)/x ,x!=0`
`k/2,x=0` is continuous of `x=0`,then
`k=` 3 (b) 6 (d) 9 (d) 12

Answer

Option (B) `K=6`

Explanation

ATQ `f(x)` is continuous at `x=0`

LHL=RHL


`\lim_{x \to 0^{-}} f(x)=\lim x \rightarrow 0^{+} f(x)`


`\lim_{x \rightarrow 0^{-}} \frac{\sin 3 x}{x}=\lim x \rightarrow 0^{+} \frac{k}{2}`


`\lim_{x \rightarrow 0^{-}} \frac{\sin 3 x}{3 x} \times 3=\lim x \rightarrow 0^{+} \frac{k}{2}`


`\Rightarrow 3= k/2`


Hence, `K=6`