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The function f(x)={x^2a\ \ \ \ \ ,\ \ \ ...

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

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Knowledge Check

  • The function f(x)=xsqrt(ax-x^2), a lt 0

    A
    increases on the interval (0,3a/4,a)
    B
    decreases on the interval (,3a/4)
    C
    decreases on the interval (0,3a/4)
    D
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  • The function f(x) = {{:(x^(2)//a, 0 le x lt 1),(a, 1 le x lt sqrt(2)),((2b^(2) - 4b)//x^(2), sqrt(2) le x lt infty):} is continuous for 0 le x lt infty , then the most suitable values of a and b are

    A
    a=1, b=-1
    B
    `a=-1, b= 1+sqrt(2)`
    C
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    D
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  • The function f(x) = 1 + x (sin x) [cos x], 0 lt x le (pi)/(2) (where [.] is G.I.F.)

    A
    is continuous on `(0, (pi)/(2))`
    B
    is strictly increasing in `(0, (pi)/(2))`
    C
    is strictly decreasing in `(0, (pi)/(2))`
    D
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