Check continuity of F(x)={[(sin x)/(x),," If "x<0],[x+1` If "x>=0`

Discuss the continuity of f(x) ={:{(sin""(1)/(x)", "x ne 0),(" "1", " x= 0):},

Discuss the continuity of f(x)={(x-a)sin(1/(x-a)),\ \ \ x!=a\ \ \ \ \ \ \ \ \ \ \ \ 0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=a at x=a

Check the continuity of the function f(x) at x=0 if f(x)={[x^(5), if x!=01, if x=0]}

Examine the continuity of f(x) at x=0 if f(x)= (sin 2x)/(2x), x ne 0

Check the continuity of f(x) at x=1 and x=2 if f(x)={0,quad if quad 0

Discuss the continuity of the function f(x)={(sin2x)/x ,ifx<0x+2,ifxgeq0

Check the continuity of the function f(x)=2x-1, if x =0

Check the continuity of f(x) at x=a if f(x)={(x^(2)-a^(2))/(x-a),quad if x!=a and 2a,quad if x=a

Check the continuity of f(x) at x=1 if f(x)={2|x|,quad if |x|

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