Let f(x) = x|x| for all x`in`R . Discuss continuity and derivability of f(X) at x = 0

Let f(x) = |x-1|+|x+1| Discuss the continuity and differentiability of the function.

Let f(x) = x+ |x|. Show that f is continuous but not derivable at x = 0

If f(x) = {|x|-|x-1|}^(2) , draw the graph of f(x) and discuss its continuity and differentiability of f(x)

If f(x) = (|X|)/(X) . Discuss the continuity at x rarr 0

Discuss continuity of f(X) = {:{(-1,x<0),(2-x,xge0):} at x = 0

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).

Let f(x) =int_0^1|x-t|t dt , then A. f(x) is continuous but not differentiable for all x in R B. f(x) is continuous and differentiable for all x in R C. f(x) is continuous for x in R-{(1)/(2)} and f(x) is differentiable for x in R - {(1)/(4),(1)/(2)} D. None of these