Math 326, March 17 -
Playing With Graphs
Section 5.1 concentrates on adding toys to our graphs. The
main trick within the chapter is to add a tracing point on the graph,
with the help of the VLOOKUP function. We began by graphing y = ax3
+ bx2 + cx + d, with a tracing point and scroll bars for a,
b, c and d.
Additional Questions
- Adapt the trace point on the cubic model to show a portion of the
tangent line instead of just a point.
- Graph y = a sin( bx + c) + d, with scroll bars for the
constants. Put y = cos2x on the same graph, and scroll
to find constants that make the two graphs equal.
- Yet Another Euler Method
- Use Euler's method to approximate the solution to the differential
equation y' = e-x - y, with initial condition y(0) =
3. Start with x0=0, y0=3 and a small
stepsize dx=0.01. We can use the DE to get y'0, the slope
at the initial point, by plugging in x0 and y0.
Now set x1=x0 + dx, y1=y0+y'0dx
. Use these to get a new slope, and repeat. Graph this
approximate solution and the real solution, y = xe-x + 3e-x. to compare the two.
Try adding a scroll bar for the initial y coordinate (note you will
need to change the real solution to match this new initial value).