Lab 01 feedback

You may still work on this lab until Sat night

Copy your existing lab into FINAL-Lab01...

Exercise 6

Use solve(...) to solve the equation $2a = ae^{kt}$ for for $t$...

Many of you did this:

var('a k t')
solve( 2*a==a*e^k*t, t)

But this is the wrong equation. Without parentheses, you're solving $$2a=ae^kt$$.

Enclose everything that goes in the exponent with $(....)$ like this:

var('a k t')
solve( 2*a==a*e^(k*t), t)

Exercise 7

Use find_root(...) to numerically approximate the third solution to the equation $7\cos(x)=x$ in the interval $[0,9]$.

In previous examples, you were shown:

find_root(7*cos(x) == x, 0, 9)

1.3733260187284693

and

find_root(7*cos(x) == x, 2, 9)

6.615965197174987

But where could that 3rd root be? You could just try other intervals that do not include the previously found solutions.

Another strategy is to graph the equations on either side of the == sign, to see if they intersect anywhere else in the domain [0,9],

plot( [ 7*cos(x),x ], x,-1,10 )

Desmos graphs and data

A number of you embedded a graph in your notebook like this: This graph has great features, like:

• $x$ and $y$ axes have labels and units (yay!)
• the data was entered correctly
• the model $y_1 ~ Mx+B$ was entered correctly, and fits well. (black line)

But it *looks* like there was a fitting problem (the purple line).

Tidy up your graph before saving and embedding. And draw attention to the most important stuff, which is usually the data:

When you're plotting data, adjust your graph so that the data is spread over as much of the screen as possible

Instead of just zooming in and out, you can use < SHIFT >-[Mouse drag] to grab just one axis and stretch/shrink it. Here you can see all the data, and that the black-line fit actually goes pretty close to that data (even though I haven't deleted the purple line that was there).

Acknowledgements

One lab had both:

• A statement acknowledging help from me and a sagemath tutorial they had found online
• And a statement the lab was finished with "no outside assistance or resources".

Let's discuss the line between plagiarism and collaboration!

Lab 03

A couple people have asked whether you need to code limits on $x$ and/or $y$ in Geogebra graphs.

No. Limits will actually get in the way of you zooming in and out to thoroughly explore a graph. However, you should zoom to an appropriate level of detail before saving / embedding your graph in your notebook, so that whatever is interesting about a graph is seen in sufficient detail.