Show that the function f(x) defined by :
`f(x)={{:((sinx)/x+cosx", "xgt0),(2", "x=0),((4(1-sqrt(1-x)))/x", "xlt0):}`
is continuous at x = 0.

If f(x)={{:((sin(a+1)x+2sinx)/x", "xlt0),(2" ,"x=0),((sqrt(1+bx)-1)/x" ,"xgt0):} is continuous at x = 0, then find the values of 'a' and 'b'.

Let f(x)={{:((sin(a+1)x+sinx)/(x)",",xlt0),(c",",x=0),((sqrt(x+bx^(2)))/(bx^((3)/(2)))",",xgt0):} If f(x) is continous at x = 0, then

if f(x)={{:((sin(p+1)x+sinx)/(x),xlt0),(x,x=0),((sqrt(x^(2)+x)-sqrt(x))/(x^(3//2)),xgt0):} is continuous at x=0 then (p,q) is

The values of a,b and c which make the function f(x)={{:(("sin"(a+1)x+"sinx")/(x),xlt0),(C,x=0),(sqrt(x+bx^(2)-sqrt("x"))/(b"x"^(3//2)),"x"gt0):} continuous at x=0 are

If the function f(x) defined by {:(f(x),=x (sin)1/x,",","for"x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0, then k =

Show that the Signum Function f:RrarrR , given by : f(x)={{:("1, if "xgt0),("0, if "x=0),("-1, if "xlt0):} is neither one-one nor onto.

If f(x) = ((1+sinx)-sqrt(1-sinx))/(x) , x != 0 , is continuous at x = 0, then f(0) is

If the function f(x), defined as f(x)={{:((a(1-xsinx)+b cosx+5)/(x^(2)),":", xne0),(3,":",x=0):} is continuous at x=0 , then the value of (b^(4)+a)/(5+a) is equal to