"Expanding the taylor series for ##f(x)##.." (See picture) is this a typo? Aren't we expanding ##f(x + \Delta x)##?(adsbygoogle = window.adsbygoogle || []).push({});

Also, when we evaluate ##f(x)## (coefficients in the expansion), are we assuming ##\Delta x = 0## by setting ##x + \Delta x## (argument of the function) equal to ##x##? Or are we just "replacing" ##x + \Delta x## by ##x##? I'm confused because usually when a function is evaluated at a particular number we just set the variable inside the argument of the function equal to that number, but when we're evaluating at "some other variable", for instance, finding ##f(x^2 + 1)## given ##f(x) = x^5##, we're not implying that ##x^2 + 1 = x^5##.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Differentials, taylor series, and function notation

**Physics Forums | Science Articles, Homework Help, Discussion**