Show that the functon given by `f(x)=(x-|x|)/(x)(x ne0)` is continuous on R-{0}

Show that f ,given by f(x)=(x-|x|)/(x)(xne0) is continuous on R - {0}

Show thatf (x) = (x-|x|)/(x),x ne 0 is continuous on 2R - {0}

Show that the function f(x)=(x)/(1+e^(1//x),x ne 0, f(0)= 0 is continuous at x = 0

Show that the function f(x) =x sub (1)/(x) , x ne 0 f(0) =0 is continuous at x = 0

Show that the function f(x) = x cos (1//x), x ne 0 f(0) = 1 is discontinuous at x = 0.

f(x)=(x)/(5)+(5)/(x)(x ne0) is increasing in

Show that the function f given by f(x)= {{:(x^3+3," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

Let a, b in R be such that the function f given by f(x)= ln |x|+bx^(2)+ax, x ne0 has extreme values at x=-1 and x=2 Statemet-I : f has local maximum at x=-1 and x=2. Statement- II: a=(1)/(2),b=(-1)/(4)

Show that the function f (x) = x ^(p) sin ((1)/(x)) x , ne 0, f (0) =0 is continuous but not differentiable at x=0 if 0 lt p le 1.

Show that f(x) = x sin ((1)/(x)), x ne 0 , f(0) = 0 is continuous at x = 0