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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 sin
by 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 agoIt 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 agoYou're basically right. Here's the graph: https://www.desmos.com/calculator/lf3xerswdy https://www.desmos.com/calculator/lf3xerswdy
- bheadmaster 4y agoAh, 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 :)