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When you blow on the mouth of an empty bottle, you may hear a "boing" sound. This phenomenon is called Helmholtz resonance. In this article, we will explain the mechanism of Helmholtz resonance.

Extending the one-variable Taylor expansion, we derive a Taylor expansion for multivariable functions. We will first discuss Taylor expansions for two-variable functions.

As a specific example of Taylor expansion, we will compute the Maclaurin expansion of e^x, sinx, and cosx. And finally, we derive Euler's formula.

Derive the Taylor expansion. The beauty of the Taylor expansion is that it allows us to express functions in polynomial form.