If `f(x)= 0,` when `x = 0=1/2-x,` when `0 < x < 1/2 =1/2.` when `x=1/2` then test the continuity of `f(x) at x=0 and x=1/2`

If f(x)=-x, when x 0=0, when x>0 then test the continuity of f(x) at x=0

A function f(x) is defined as f(x)= {:{(1," when " x != 0),(2," when " x = 0 ):} does the Limit of f(x) as x to 0 exist ? Explain your answer .

If f(x) = {(|sinx|/x, when x=0),(1, when x!=0):} then examine the continuity of the function at x=0.

Draw the graph of the following signum function : f(x)=1," when "x gt0 =0," when "x=0 =-1," when "x lt0 Find the domain and range of f(x) from the graph.

Let f(x) =x^(p) cos (1/x) , when x ne 0 and f(x)=0 , when x=0 . Then f(x) will be differentiable at x=0 , if

If f(x)={(2x+3, "when x" lt 0),(0, "when x"=0),(x^2+3, "when x"gt 0):} Discuss continuity at x=0.

If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

If the function f(x) = {{:((sin(k+1)x + sinx)/x, "when " x lt 0),(1//2, "when " x=0 is),((x+2x^(2))^(1//2)/(2x^(3//2)), " when " x gt 0):} continous at x=0 , then the value of k is-