#34, p. 70

Clear[f,x]
f[x_]:=(Sqrt[3+x]-Sqrt[3])/x;
Simplify[f[x]]
f[{-.1,-.01,-.001,-.0001,.0001,.001,.01,.1}]
Plot[f[x],{x,-1,1}]
Limit[f[x],x->0]
N[%]

#50, p. 71

Clear[g,x]
g=Piecewise[{{x,x<1},{3,x==1},{2-x^2,x≤2}},x-3]
Plot[g,{x,-1,4}]
Limit[g,x->0]
N[%]

f[x_]:=(x^2-4x)/(x^2-3x-4);
Simplify[f[x]]
Plot[f[x],{x,3,5}]
Limit[f[x],x->4]

Plot[f[x],{x,-2,0}]
Limit[f[x],x->-1,Direction->1]
Limit[f[x],x->-1,Direction->-1]

f[u_]:=(Sqrt[4u+1]-3)/(u-2);
Simplify[f[u]]
Plot[f[u],{u,1,3}]
Limit[f[u],u->2]