If `f(x)={(sin3x)/x,w h e nx!=0 1,w h e nx=0dot` Find whether `f(x)` is continuous at `x=0`

Explanation

`f(x)= (sin3x)/x`

For the continuity at `x=0`

`f(0)=1`

`text { LHL }=lim _{x -> 0} f(x) `

`text{LHL}=lim _{h -> 0} f({O}-h) `

`text{LHL}=lim _{h -> 0} (sin3(0-h))/{0-h}`

`text{LHL} = lim _{h -> 0} (sin(-3h))/{-h}= lim _{h -> 0} 3times (sin(-3h))/{-3h}=3`

Now,

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