`f(x)={[x^(2)+3,,x!=0],[1,,x=0]:}` is not continous at x=0

If f (x) = [{:((ae^(sin x )+be ^(-sinx)-c)/(x ^(2)),,, x ne0),(2, ,, x =0):} is continous at x=0, then:

If f (x)= {{:((x-e ^(x)+1-(1-cos 2x))/(x ^(2)), x ne 0),(k,x=0):} is continous at x=0 then which of the following statement is false ?

The value of k(k f(x)= {((1-cos kx)/(x(sin x)),x!=0 or (1)/(2),x=0} ,is continous at x=0 is :

If f(x) = {{:(x cos 1/x, x ne 0),(k ,x =0):} is continous at x=0, then

If f(x) = {{:(sin1/x, x ne 0),(k, x =0):} , is continous at x=0, then k is equal to-

Let f(x)= {(((xsinx+2cos2x)/(2))^((1)/(x^(2))),,,,xne0),(e^(-K//2),,,,x=0):} if f(x) is continous at x=0 then the value of k is

f(x)={((Sin(a+1)x+Sin2x)/(2x),,x lt 0),(b,,x=0),((sqrt(x-bx^3)-sqrtx)/(bx^(5/2) ), , xgt0):} , f(x) is a continous at x=0 then abs(a+b) is equal to

Le t f(x) ={{:((sinpix)/(5x)",",xne0),(" "k",",x=0):} if (x) is continous at x=0 , then k is equal to