Section 1.5: Homework
Calculus I
Andy Long

(* Section 1.5 Homework, #28, 38, 44, 46 *)
Clear[a,b,f,m0,m,c,v];

(* Exercise 28, p. 65: *)
f[x_]:=Sin[x]/Sin[Pi x] (* note that this function is even, so we only need to check one side. *)
f[{.1,.01,.001,.0001}]
Plot[f[x],{x,-1,1},PlotRange->{-0.5,1}]

(* Exercise 38, p. 65: *)
f[x_]:=(x^2+1)/(3x-2x^2)
Solve[3x-2x^2==0,x]
Plot[f[x],{x,-2,3},PlotRange->{-3,3}]

#44, p. 61:

m0=1; (* we'll make m0 a "unit mass" *)
c=300; (* The speed of light is 299 792 458 m/s -- so approximately 300 million m/s *)
m[v_]:=m0/Sqrt[1-v^2/c^2]
Limit[m[v],v-> c, Direction->1]
Plot[m[v],{v,0,290},PlotLabel->"Mass becomes infinitely large as speed approaches c"]

#46, p. 61:

Clear[L,f,x]
f[x_]:=(x^3-1)/(Sqrt[x]-1)
L=Limit[f[x],x-> 1]
Plot[{L-.5,f[x],L+.5},{x,0,2},PlotLabel->"How close to 1 does x have to get to be within .5 of the limit, 6?"]

Plot[{L-.5,f[x],L+.5},{x,1-.1,1+.1},PlotLabel->"How close to 1 does x have to get to be within .5 of 4?"]

Solve[f[x]==L+.5,x,Reals]
Solve[f[x]==L-.5,x,Reals]