Homework Section 1.4: 2, 7

Univariate Calculus
Andy Long

#2, p. 49

xs={36,38,40,42, 44}
ys={2530, 2661, 2806, 2948, 3080}
ListPlot[Transpose[{xs,ys}]]

slopes=(ys-ys[[4]])/(xs-xs[[4]])
N[slopes]

good guess by using the two points surrounding the point of interest. All of the slopes were pretty similar, which suggests that heart rate is fairly constant. We might ask if the heart rate is on the decline, however....

slope=N[(ys[[5]]-ys[[3]])/(xs[[5]]-xs[[3]])]

#7: don’t forget units on your answers (meters/second)

xs={0,1,2,3,4,5}
ys={0,1.4,5.1, 10.7, 17.7, 25.8}
ListPlot[Transpose[{xs,ys}]]

AV[t1_,t2_]:=(ys[[t2+1]]-ys[[t1+1]])/(xs[[t2+1]]-xs[[t1+1]])
AV[1,3]
AV[2,3]
AV[3,5]
AV[3,4]

slope=N[(ys[[5]]-ys[[3]])/(xs[[5]]-xs[[3]])]