Mathematica Tool 1

This Mathematica notebook is designed to be used in connection with the zooming plots in Section 4.8

We are plotting a portion of the graph from y=(t^2) from 1 from 1+Δ t for various values of Δt together with the tangent line at t=1. The corresponding Δy is calculated.  Zoom in by plotting the graphs with Δt=1, Δt=.1, Δt=.01, and  Δt=.001 (or choose your own values for Δt ).

y[t_]:=(t^2)

Modify the value of Δt in the line below. Then plot the corresponding graph.

Δt =1;

Δy=y[1+Δt]-y[1];
T[t_]:=y[1]+y'[1](t-1);
Plot[{y[t],T[t]},{t,1,1+Δt},PlotRange->{{1,1+Δt},{y[1],y[1]+Δy}}]
Print["Δt,",Δt]
Print["Δy,",Δy]