56 Which of the following does not define a metric on the set of all real members?

(A) F(x,y)= 0 if x=y and 2 if x!=y

(b) F(x,y)= min{ abs(x-y),1}

(c) F(x,y)= abs(x-y)/3

(d) F(x,y)= abs(x-y)/(abs(x-y)+1)

(e) F(x,y)= (x-y)^2

I can understand (a) (c) and (d) but how to know (b) is a metric but (e) is not.

57 The set of real numbers x for which the series Sum ( n!*x^(2n)/n^(n)*(1+x^(2n))

converges is

(a) {0} (b) {x:-1<x<1} (c) {x:-1<=x<=1} (d) {x:-sqrt(e)<=x<=sqrt(e)} (e) R

I used the ratio test to get the limit but there should be a trick in doing this and I can't figure it out.

63 If f is the function defined by f(x)= x*exp(-x^2-x^(-2) if x!=0 and =0 if x=0, at how many values of x does the graph of f have a horizontal tangent line?

Please help, thanks a lot.