Would anyone know an analytical solution to finding the root of
$$ f(x) = \sin(x^2) - e^x $$
in $[-1,1]$? I'm writing a simple root finding program and thought I'd try this as a test case, but stumped myself trying to find a root to compare with!
2026-04-05 21:28:43.1775424523
Root of function involving trig and exponential
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I doubt there's any closed form. Wolfram Alpha says $x \approx -0.714968969189656...$ is a root in that range; http://www.wolframalpha.com/input/?i=roots+of+sin%28x%5E2%29+-+e%5Ex.