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.`

Show that the function f(x) given by f(x)={(sinx)/x+cosx ,x!=0 and 2,x=0 is continuous at x=0.

Find the value of ' a^(prime) for which the function f defined by f(x)={asinpi/2(x+1),\ \ \ xlt=0(tanx-sinx)/(x^3),\ \ \ x >0 is continuous at x=0 .

Find the value of a for which the function f defined by f(x)={asinpi/2(x+1), ,xlt=0(tanx-sinx)/(x^3),x >0" is continuous at x=0

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 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

Find the value of a for which the function f defined by f(x)={asin(pi/2)(x+1),xlt=0(tanx-sinx)/(x^3),x >0" is continuous", at x=0

Show that the Signum function f:R->R , given by f(x)={(1,xgt0),(0,x=0),(-1,xlt0)) is neither one-one nor onto