Recent content by wizkhal

Hello all, Recently I've found something very interesting concerning Taylor series. It's a graphical representation of a second order error bound of the series. Here is the link: http://www.karlscalculus.org/l8_4-1.html My question is: is it possible to represent higher order error bounds...

They use this equation in so many texts... It seems that these texts are massively erroneous...

But how it can become '=' ? I know that the error will become smaller and smaller as 'h' goes to zero, but my way of thinking is that we can never replace '\approx' with '='... Even if 'h' = 0,000000000000(...)0001 the error will always exist. I just want to be precise.

For tiny h, f(x+h) = f(x) + hf'(x) ?? Hi all I've been reading about proof of the chain rule and something is making me not sleep at night.. How is that possible that: "for tiny h, f(x+h) = f(x) + hf'(x)" ? Even if 'h' is ultra-small, then "f(x+h)" will always differ from "f(x) +...

Thank you for the answer. Can't I continue with this difference quotient in such a way (with factoring 'h' out) ? : \lim_{h \rightarrow 0} \frac{5^h - 1}{h} = \lim_{h \rightarrow 0} \frac{e^{hln5} - 1}{h} = \lim_{h \rightarrow 0} \frac{(1 + hln5) - 1}{h} = \lim_{h \rightarrow 0}...

Hi all, I'm a beginner in calculus so my question might be stupid. When a function is differentiable, then in difference quotient one can always factor 'h' out in the numerator, even if the function is exponential and 'h' is in the exponent. Is some magic behind this or something else? I've read...