1.

Let `f(x) =` Degree of `(u^(x^2) + u^2 +2u + 3).` Then, at` x=sqrt2, f(x)` isA. continuous but not differentiableB. differentiableC. dicontinuousD. none of these

Answer» Correct Answer - A
We have
`f(x)="Degree of "(u^(x^(2))+u^(2)+2u+3)`
`Rightarrow f(x)={{:(,x^(2),x gt sqrt2),(,2,x le sqrt2):}`
`therefore underset(x to sqrt2)lim f(x)=2=f(2)` and
`underset(x to sqrt2^(+))limf(x)=underset(x to sqrt2)lim =(sqrt2)^(2)=2 `
`therefore underset(x to sqrt2^(-))limf(x)=underset(x to sqrt2^(+))lim f(x)=f(sqrt2) `
So, f(x) is continuous at `x=sqrt2`
Now, `("LHD at x=sqrt2")=((d)/(dx)(2))_(x=sqrt2)=0`
`("RHD at x=sqrt2")=((d)/(dx)(x^(2)))_(x=sqrt2)=(2x)_(x=sqrt2)=2sqrt2`
So, f(x) is not differentiable at `x=sqrt2`


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