How to find the error or remainder of a series

If you need to find the sum of a series, but you don’t have a formula that you can use to do it, you can instead add the first several terms, and then use the integral test to estimate the very small remainder made up by the rest of the infinite series. The sum of the series is usually the sum of the first several terms, plus a very smaller error that you can estimate.

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Partial derivatives in two variable functions

Finding derivatives of a multivariable function means we’re going to take the derivative with respect to one variable at a time. For example, we’ll take the derivative with respect to x while we treat y as a constant, then we’ll take another derivative of the original function, this one with respect to y while we treat x as a constant.

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Finding inverse trig derivatives

To avoid confusion between negative exponents and inverse functions, sometimes it’s safer to write arcsin instead of sin^(-1) when you’re talking about the inverse sine function. The same thinking applies to the other five inverse trig functions.

Simple equations with subscripts

Why use subscripts instead of different variables? Well, the variables in science often represent something specific. For example, P stands for pressure and in some equations you’ll have more than one pressure represented. In that case we use subscripts: P_1, P_2, P_3, and so on.