Homework, 14.4
Spring, 2016
Andy Long

#14, 22, 37

#14, p. 946

f[x_,y_]:=Sqrt[x+E^(4y)]
xp=3
yp=0
dx=1
dy=1
fx[x_,y_]=D[f[x,y],x]
fy[x_,y_]=D[f[x,y],y]
L[x_,y_]:=f[xp,yp]+fx[xp,yp](x-xp)+fy[xp,yp](y-yp)
Plot3D[{f[x,y],L[x,y]},{x,xp-dx,xp+dx},{y,yp-dy,yp+dy}]

#22, p. 946

vp=40
tp=20
dv=3
dt=4
fv=(40-17)/(50-30)
ft=(31-25)/(30-15)
L[v_,t_]:=28+fv(v-vp)+ft(t-tp)
Simplify[L[v,t]]
L[vp+dv,tp+dt]
N[%]
Plot3D[L[v,t],{v,vp-dv,vp+dv},{t,tp-dt,tp+dt}]

#37, p. 947

tension[R_,r_]:=m g R /(2r^2+R^2)
Rp=3
rp=0.7
dR=.1
dr=.1
fR[R_,r_]=D[tension[R,r],R]
fr[R_,r_]=D[tension[R,r],r]
dt=fR[Rp,rp]dR+fr[Rp,rp]dr