Mathematica plots for functions sketched in Lab 2
Exp[x] is the natural exponential (E^x), Log[x] is the natural logarithm.  The Abs[x] 
function is the absolute value of x. Entering PlotRange->{a,b} as the last argument to 
the Plot[] function sets the y limits. Useful approximations are given at the bottom.

f[x_]:= Exp[2x] - Exp[x]

Plot[f[x],{x,-5,0.5},PlotRange->{-0.3,0.3}]

g[x_]:= ((Log[Abs[x]])/(x^2))

Plot[g[x],{x,-5,5},PlotRange->{-0.2,0.2}]

h[x_]:= (x^2-3)Exp[-x]

Plot[h[x],{x,-2,5},PlotRange->{-6,1}]

u[x_]:=((x^3)/((x-3)(x+5)))

Plot[u[x],{x,-20,10},PlotRange->{-20,10}]

v[x_]:= ((Sin[x])/(2+Cos[x]))

Plot[v[x],{x,-2π,2π},PlotRange->{-0.6,0.6}]

N[E]

N[E^(5/3)]

N[E^(5/6)]

N[E^(1/2)]

N[Log[1/2]]

N[Log[1/4]]

N[(Sqrt[5])]

N[ArcCos[-1/2]]