Exam 2

MAT 129, Spring 2018

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Name:

Problem 1:

f[x_]:=Cos[x]/(x^2-3)
Together[f'[x]]
g[x_]:=Cos[x^2-3]
g'[x]
p[x_]:=(Cos[x])^2-3
p'[x]
q[x_]:=Cos[x](x^2-3)
Together[q'[x]]

Problem 3:

thickness=1
V[r_]:=Pi r^2 thickness
D[V[r[t]],t]
1000/(2 π 25)
rprime=1000000/(2 π 2500)
N[%]
(2 π 25)rprime
aprime=(2 π 2500)rprime
N[%]

Problem 4:

Clear[x,y]
soln=Solve[D[x^2+y[x]^2==1,x],y'[x]]
yp[x_]=y'[x]/.First[First[soln]]
soln=Solve[x^2+y^2==1,y]
y[x_]=-First[y/.First[Second[soln]]]
yp[x]
yp[1/2]
N[%]

Problem 5:

Plot[{(x^2-3x+2)/(x+1),x-4},{x,-10,10},PlotRange->{{-10,10},{-15,5}},PlotLabel->"Graph of f(x)"]
Plot[{(2x^2-3x+2)/CubeRoot[x^6+1],2},{x,-10,10},PlotRange->{{-10,10},{0,5}},PlotLabel->"Graph of g(x)"]
Plot[{Sqrt[x^2+2x-2],x+1,-(x+1)},{x,-10,10},PlotRange->{{-10,10},{0,10}},PlotLabel->"Graph of h(x)"]

Problem 6:

Plot[Cos[x]/(x^2+1),{x,-4,4},PlotRange->{{-4,4},{-1,1}},PlotLabel->"Graph of f'(x)"]
g[x_]=D[Cos[x]/(x^2+1),x]
Plot[g[x],{x,-4,4},PlotRange->{{-4,4},{-1,1}},PlotLabel->"Graph of f''(x)"]
Plot[NIntegrate[Cos[x]/(x^2+1),{x,0,t}],{t,-4,4},PlotRange->{{-4,4},{-1,1}},PlotLabel->"Graph of F(x), F(0)=0"]

Problem 7:

f[x_]:=x/(x^2+1)
Plot[f[x],{x,-3,3},PlotRange->{{-2,2},{-0.5,0.5}},PlotLabel->"Graph of f(x)"]
Together[f'[x]]
Together[f''[x]]
(* Plot[Sqrt[-1]x/(x^2+1),{x,-3,3},PlotRange->{{-2,2},{-0.5,0.5}},PlotLabel->"Graph of f(x)"] *)