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Technical Definition: A way to approximate (very) smooth functions (for which derivatives up to high orders exist and are continuous) Simple Definition: Taylor series is the infinite sum of all the terms for...

Prerequisite for addition formula: https://www.youtube.com/watch?v=iHZmi2MHqWc Proof of formula for sin(A+B): https://www.youtube.com/watch?v=BEETggUVMrY Proof of formula for cos(A+B): https://www.youtube.co...

Here we have a product of two things, so we will be using the product rule of differentiation. This is: for y=u(x)v(x), where u(x) and v(x) are funtions of x, dy/dx = u'(x)v(x) + u(x)v'(x). So in this case l...

We can't integrate cos^2(x) as it is, so we want to change it into another form. We can easily do this using trig identities . 1) Recall the double angle formula: cos(2x) = cos^2(x) - sin^2(x). 2) We also kn...

There's a nice trick here you can do, treat the equation as 1*ln(x) then intergrate by parts. Differentiating ln(x) gives 1/x, while intergrating 1 gives x So your left with a much easier intergration x ln(x...