Homework, section 2.1

Univariate Calculus
Andy Long

#18, p. 111

l[x_]:=4*(x-5)-3
Plot[l[x],{x,3,7},AxesLabel->Automatic, PlotLabel->"#18, p. 111"]

#19, p. 111

l[x_]:=4x-5
l[2]
l'[2]
Plot[l[x],{x,0,4},AxesLabel->Automatic, PlotLabel->"#19, p. 111"]

#27, p. 112

Clear[a,h]
f[x_]:=3x^2-4x+1
ratio=(f[a+h]-f[a])/h
Simplify[ratio]
Limit[ratio,h->0]

#33, p. 112

f[x_]:=x^10
x0=1 
y0=f[x0]
m=f'[x0]
Limit[((1+h)^10-1)/h,h->0]
l[x_]:=m(x-x0)+y0
Plot[{f[x],l[x]},{x,0,1.1}
,PlotRange->{0,2}
,AxesLabel->Automatic
, PlotLabel->"#33, p. 112"
]

#34, p. 112

Clear[a,h]
f[x_]:=x^(1/4)
a=16
ratio=(f[a+h]-f[a])/h
Simplify[ratio]
Limit[ratio,h->0]