The function `f(x)={(x^2)/a\ \ \ \ ,\ \ \ if\ 0lt=x<1,\ \ \ \a\ \ \ ,\ \ \ if\ 1lt=x` is continuous then find the value of constent term

Explanation

Since, `f` is continuous for `0 leq x

`lim _{x rightarrow 1^{-}} frac{x^{2}}{a}=a`


`therefore {a}=pm 1`


Since, `f` is continuous at `x=sqrt{2}`.


`lim _{x rightarrow sqrt{2}} frac{2 b^{2}-4 b}{x^{2}}=a`


`therefore frac{2 b^{2}-4 b}{2}=a`


`Rightarrow {b}^{2}-2 {~b}={a}`


When `a=1, b^{2}-2 b=1`


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