5 ms·

Also a good question to test intuition is being asked to sketch e^sin(x) and sin(e^x).

bheadmaster 4y ago
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. Either that, or my mathematical intuition has got rusty from years of code monkeying.
- soVeryTired 4y ago
  It wouldn’t look too dissimilar to a standard sinusoid, just shifted upwards a bit. In the range [-1, 1], e^x is reasonably similar to 1 + x.
- madcaptenor 4y ago
  You're basically right. Here's the graph: https://www.desmos.com/calculator/lf3xerswdy https://www.desmos.com/calculator/lf3xerswdy
  - bheadmaster 4y ago
    Ah, now it makes sense. The slope of the sine is "squashed" down by the x->e^x mapping. Perhaps (regularly) seeing functions plotted on graphs is a necessary precondition to maintain intuition :)
jhart99 4y ago
Seems a little much for a regular calculus class. Wouldn't that fit better in a complex analysis class?
- jetunsaure 4y ago
  No, this would be a good exercise for first-year calculus. It's a very reasonable question, nothing out of the ordinary.
  - KMag 4y ago
    In fact, I was taught the graphical intuition via a few days of these sorts of exercises, before being introduced to the formulas. It worked really well, at least for 9th grade students in an acceleration program at the University of Minnesota (UMTYMP).
anthk 4y ago
TCL, package require math, a few lines of puts writting to a file and then gnuplot that.
- yberreby 4y ago
  How does that test intuition?
- EForEndeavour 4y ago
  That's one of many ways to check one's answer. The whole point is to be able to intuit a rough sketch of what the graph should be, not to use software tools to build a pixel-perfect render of the plot.
h4ch1 4y ago
I really enjoy https://graphtoy.com/ https://graphtoy.com/ by the great Inigo Quilez to quickly verify my mental models for mathematical equations
- Timon3 4y ago
  Thank you for sharing that! I usually go with Desmos, but for a quick plot this seems even nicer, especially given the time coordinate!

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. Either that, or my mathematical intuition has got rusty from years of code monkeying.

soVeryTired 4y ago
It wouldn’t look too dissimilar to a standard sinusoid, just shifted upwards a bit. In the range [-1, 1], e^x is reasonably similar to 1 + x.
madcaptenor 4y ago
You're basically right. Here's the graph: https://www.desmos.com/calculator/lf3xerswdy https://www.desmos.com/calculator/lf3xerswdy
- bheadmaster 4y ago
  Ah, now it makes sense. The slope of the sine is "squashed" down by the x->e^x mapping. Perhaps (regularly) seeing functions plotted on graphs is a necessary precondition to maintain intuition :)

jhart99 4y ago

Seems a little much for a regular calculus class. Wouldn't that fit better in a complex analysis class?

jetunsaure 4y ago
No, this would be a good exercise for first-year calculus. It's a very reasonable question, nothing out of the ordinary.
- KMag 4y ago
  In fact, I was taught the graphical intuition via a few days of these sorts of exercises, before being introduced to the formulas. It worked really well, at least for 9th grade students in an acceleration program at the University of Minnesota (UMTYMP).

anthk 4y ago

TCL, package require math, a few lines of puts writting to a file and then gnuplot that.

yberreby 4y ago
How does that test intuition?
EForEndeavour 4y ago
That's one of many ways to check one's answer. The whole point is to be able to intuit a rough sketch of what the graph should be, not to use software tools to build a pixel-perfect render of the plot.

h4ch1 4y ago

I really enjoy https://graphtoy.com/ https://graphtoy.com/ by the great Inigo Quilez to quickly verify my mental models for mathematical equations

Timon3 4y ago
Thank you for sharing that! I usually go with Desmos, but for a quick plot this seems even nicer, especially given the time coordinate!