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

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

Consider function f(x)={x{x}+1,\ \ \ \ \ \ \ \ \ \ \ \ 0lt=x<1 2-{x},\ \ \ \ 1lt=xlt=2\ \ \ where {x}: fractional part function of x . Statement-1: Rolles Theorem is not applicable to f(x) in [0,2] Statement-2: f(0)\ !=f(2)

The points of discontinuity of the function f(x)={2sqrt(x)\ \ \ ,\ \ \ 0lt=xlt=1 ,\ \ \4-2x\ \ \ ,\ \ \ 1< x

The function f(x) is defined by f(x)={x^2+a x+b\ \ \ ,\ \ \ 0lt=x 4 f is continuous them determine the value of a and b

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

The primitive of the function f(x)= x | cos x| , when pi/2 lt x lt pi is given by

The function f(x)= {(5x-4 ", " 0 lt x le 1 ),( 4x^3-3x", " 1 lt x lt 2):}

The function f(x)={{:(,(x^(2))/(a),0 le x lt 1),(,a,1le x lt sqrt2),(,(2b^(2)-4b)/(x^(2)),sqrt2 le x lt oo):} is a continuous for 0 le x lt oo . Then which of the following statements is correct?