Let `f(x)={{:((alphacotx)/(x)+(beta)/(x^(2))",",0ltxle1),((1)/(3)",",x=0):}`
If f(x) is continuous at x =0, then the value of `alpha^(2)+beta^(2)` is

Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):} . If f(x) is continuous at x=0 then the value of alpha^2+beta^2 is

Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):} . If f(x) is continuous at x=0 then the value of alpha^2+beta^2 is

Let f(x)={((alpha cotx)/x+beta/x^2,0<|x|lt=1),(1/3,x=0)) If f(x) is continuous at x=0 then the value of alpha^2+beta^2 is 1 b. 2 c. 5 d. 9

Let f(x)={{:((1-cos2ax)/(xsin2x),"when " xne0),(" " (1)/(2),"when " x =0):} If f (x) is continuous at x = 0 , find the value of alpha .

Let f(x)={{:(3x-4,0lexle2),(2x+1,2ltxle9):} If f is continuous at x = 2, then what is the value of l ?

Let f : R rarr R be defined as f(x) = {{:((x^(3))/((1-cos 2x)^(2)) log_(e)((1+2x e^(-2x))/((1-x e^(-x))^(2))),",",x ne 0),(alpha,",", x =0):} . If f is continuous at x = 0, then alpha is equal to :

If alpha, beta are roots of x^(2)-2x-1=0 , then value of 5alpha^(4)+12beta^(3) is

{:(f(x),=x^(2)+alpha,",","for"x ge 0),(,=2sqrt(x^(2)+1)+beta, ",","for"x lt 0):} is continuous at x = 0 and f((1)/(2))=2 then alpha^(2)+beta^(2) is

If {:(f(x),=x^(2)+alpha,",","for"x ge 0),(,=2sqrt(x^(2)+1)+beta, ",","for"x lt 0):} is continuous at x = 0 and f((1)/(2))=2 then alpha^(2)+beta^(2) is