MAT128 Homework, section 1.5

Univariate Calculus
Andy Long

#12

Plot[Piecewise[{{1+Sin[x],x<0},{Cos[x],x≤Pi},{Sin[x], x>Pi}}],{x,-2,5}]

#16: This is just one example, but it’s consistent with the demands imposed.

p1=Plot[Piecewise[{{1-x,x<3},{5-x,x>3}}],{x,-2,5}];
p2=ListPlot[{{0,-1},{3,1}},PlotStyle->{Thick,PointSize[Large]}];
{m1}=Graphics/@{Circle[{0,0},.02]};
p3=ListPlot[{{0,1},{3,-2},{3,2}},PlotMarkers->Table[{s,0.05},{s,{m1}}]];

Show[p1,p2,p3]

#20

f[x_]:=(x^2-2x)/(x^2-x-2)
Plot[f[x],{x,-2,0}]
(* From the right *)
list={0,-.5,-.9,-.95,-.99,-.999}
 TableForm[Table[{x,f[x]},{x,list}]]
(* From the left : *)
list={-2,-1.5,-1.1,-1.01,-1.001}
 TableForm[Table[{x,f[x]},{x,list}]]
Limit[f[x],x-> -1]

#23

f[x_]:=(Sqrt[x+4]-2)/x
Plot[f[x],{x,-.3,.3}]
(* From the left: *)
list={-.3,-.1,-.01,-.001,-.0001}
 TableForm[Table[{x,f[x]},{x,list}]]
(* From the right: *)
 TableForm[Table[{x,f[x]},{x,-list}]]
Limit[f[x],x-> 0]
g[x_]:=(x*(Sqrt[1+3x]+1))/((1+3x)-1)
g[x]
Limit[g[x],x-> 0]

#24

f[x_]:=Tan[3x]/Tan[5x];
Plot[f[x],{x,-.3,.3}]
(* From the left: *)
list={-.3,-.1,-.01,-.001,-.0001}
 TableForm[Table[{x,f[x]},{x,list}]]
(* From the right: *)
 TableForm[Table[{x,f[x]},{x,-list}]]
Limit[f[x],x-> 0]
Limit[f[x],x-> 0,Direction->-1]