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Comment by xnorswap | Hacker News Reader

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.

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

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.

You're basically right. Here's the graph: https://www.desmos.com/calculator/lf3xerswdy

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 :)

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

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

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.

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).

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

How does that test intuition?

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.

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