Find the value of the k if the function `f(x)={(kx^2, x ge 1),(4, x<1):}` is continuous at x =1

Find the value of a for which the function f(x) = a sin x + (1)/3 sin 3x has an extremum at x =pi/3 .

Find the value of m, such that the function f(x){{:(m(m^(2)-2x)","," x" lt0),(cos .x ","," x" ge0):} is continuous at x=0.

Find the value of kappa , so that the function f(x)={{:((x^(3)+x^(2)-16x+20)/((x-2)^(2))","," if" x ne2,),(kappa","," if" x=2,):} is continous at x=2

Find the value of k for which f(x)={(2x+k,0lexle 1),(3x, x>1):}, "" is continuous at x=1

Find the domain and range of the real function f(x)=(x^2)/(x^2-1) .

Find the intervals in which the function f(x)=2x^(3) + 9x^2 + 12x + 20 is increasing

Find the value of k for which f(x)={((kcosx)/(pi-2x), "" xnepi/2),(3",", ""x=pi/2):} is continuous at x=1