101–110 of 163 posts
Earlier quoted context omitted.
Also a good question to test intuition is being asked to sketch e^sin(x) and sin(e^x).
TCL, package require math, a few lines of puts writting to a file and then gnuplot that.
Earlier quoted context omitted.
Also a good question to test intuition is being asked to sketch e^sin(x) and sin(e^x).
Intuition tells me e^sin(x) would look similar to an ordinary sinusiod, except its range would be between e^-1 and e, and its shape would not be smooth as a sinusiod. I have no idea what the shape would look like, and I'm a visual learner when it comes to mathematics. I think most of these questions are not measuring intuition per se, but rather has the tested person previously seen such functions plotted on a graph.…
Here's another exercise (resp. exam question) that tests understanding: given a sketch of a curve in a graph, roughly sketch the derivative (or integral). The number of otherwise good students who go "but I can't do the derivative without the formula?" suggests we need more questions like this.
The problem is that most teachers cannot come up with questions that go outside the small number of cases which the student trains on. I mean, coming up with fundamentally new questions is very hard work once the low hanging fruit is gone.
Here's another exercise (resp. exam question) that tests understanding: given a sketch of a curve in a graph, roughly sketch the derivative (or integral). The number of otherwise good students who go "but I can't do the derivative without the formula?" suggests we need more questions like this.
I learned basics of calculus as a teenager making animations with a pirated copy of Adobe After Effects. It’s a motion graphics package where you can animate any property of an element over time using both absolute values and velocity curves (i.e. the derivative). It shows both curves next to each other, so you can tweak either and see how the other changes. Seeing graphics animate according to a derivative that you…
(The last time I taught math was vector calc 4 years ago. The last time I taught the first semester intro to calc was 30 years ago OMG-LOL.)
Current Calc 2 student here. I would be braindead approaching this problem honestly, I don't think I'd even know how to begin; I'm hoping that's normal. Why would the exponent be equal to x/2 - floor(x/2) be equal to x/2 on the interval [0, 2)? And how does the graph of x/2 - floor(x/2) imply anything about the behavior of e^(x/2 - floor(x/2))? I'm hoping I just haven't learned enough yet?
Earlier quoted context omitted.
Seems a little much for a regular calculus class. Wouldn't that fit better in a complex analysis class?
No, this would be a good exercise for first-year calculus. It's a very reasonable question, nothing out of the ordinary.
Earlier quoted context omitted.
Also a good question to test intuition is being asked to sketch e^sin(x) and sin(e^x).
Intuition tells me e^sin(x) would look similar to an ordinary sinusiod, except its range would be between e^-1 and e, and its shape would not be smooth as a sinusiod. I have no idea what the shape would look like, and I'm a visual learner when it comes to mathematics. I think most of these questions are not measuring intuition per se, but rather has the tested person previously seen such functions plotted on a graph.…
Here's another exercise (resp. exam question) that tests understanding: given a sketch of a curve in a graph, roughly sketch the derivative (or integral). The number of otherwise good students who go "but I can't do the derivative without the formula?" suggests we need more questions like this.
Day 1 of the class: The derivative calculates the slope of a function
Day 2: The integral calculates the area under the curve of the function
Days 3-89: Rote exercises deriving and integrating increasingly obscure functions
Day 90: Final Exam
Spending a few days at the end re-exploring the "big picture day-1" to tie together all of the various strands of knowledge you accumulate over the semester would have made all of it so much more effective.
Slightly off-topic: didn't know what ⌊x/2⌋ is Google: x squared (???) GPT: The expression ⌊x/2⌋ represents the greatest integer that is less than or equal to x/2. It is called the floor function of x/2. For example, if x=5, then ⌊x/2⌋ = ⌊5/2⌋ = 2. If x is an even integer, then ⌊x/2⌋ = x/2. If x is an odd integer, then ⌊x/2⌋ = (x-1)/2.
Here's another exercise (resp. exam question) that tests understanding: given a sketch of a curve in a graph, roughly sketch the derivative (or integral). The number of otherwise good students who go "but I can't do the derivative without the formula?" suggests we need more questions like this.
The problem is that most teachers cannot come up with questions that go outside the small number of cases which the student trains on. I mean, coming up with fundamentally new questions is very hard work once the low hanging fruit is gone.