Let
`f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):}`
Test whether
f(x) is differentiable at x=0

Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x) is differentiable at x=0

Consider f(x)={(x^2/|x|, x ne 0),(0, x=0):}

f(x)=5x-4 (0ltxle1) =4x^2-3x (1ltxlt2) test whether f(x) is differentiable at x=1

Let f(x)={(x^2|cos"pi/x|, x ne0),(0, x=0):} , x in R , then f is

f(x) = {(|x+1|/(x+1),when x!= -1),(0, when x = -1):} Test whether f(x) is continuous or not at x= -1

Let f(x)={((sin pix)/(5x),"when "x ne 0),(k,"when "x=0):} If f(x) is continuous at x=0, then the value of k is -

Let f(x)={(x^2|cos"pi/x|,xne0),(0,x=0):}

Let f (x+(1)/(x))= x^(2) +(1)/(x^(2)) , x ne 0, then the value of f (x) is-

Let g: RR to RR be a differentiable function with g(0)=0,g'(0)=0 and g'(1)ne0 . Let f(x)={{:((x)/(|x|)g(x)", "xne0),(0", "x =0):}" and "h(x)=e^(|x|)" for all "x inRR. Let ("foh")(x) denote f(h(x)) and ("hof")(x) denote h(f(x)) . Then which of the following is (are) true?