2015年1月6日 · now you are back to figuring out the number of times $\sin(x+h)$ and $\cos(x)$ are identical for $0 \le h ...

2018年5月9日 · First of all, it is not true that $\sin(x)\over x$ is $1$. In fact, this is never true (note that $\sin(0)\over 0$ is undefined).

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Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …

Should have been $$\tanh(x) = \dfrac{e^x-e^{-x}}{e^x+e^{-x}}$$ Same with your other two functions. There are many similarities and differences between hyperbolic functions and trig …

2017年12月11日 · $\sin(x)=x-\dfrac{x^3}{3!}+\dfrac{x^5}{5!}+r_5(x)$ is the fifth order expansion. Similarly, for the cosine you would have First term $1$, second term $-\dfrac{x^2}2$, third term …

2015年11月8日 · $\begingroup$ There is a way... it just mirrors the proof that $\sin' = \cos$. You'll end up with something very close to the classical $\frac{\sin x}{x}$ in the proof that will require …

Taylor theorem doubt(sin(x+h)) Ask Question Asked 11 years, 3 months ago. Modified 11 years, 3 months ago.

2021年6月18日 · I was just proving the continuity of the function $\sin(x)$ with $|f(x_0+h) - f(x_0) |$ and in the proof I had to use the fact that $\sin^2(h) + \cos^2(h) = 1 \iff \cos^2(h) - 1 = …

Derive $\sin{ix}=i\sinh{x}$ from $(5)$. What is $\sin{i}$? $$\cos{x}=\frac{1}{2}\left(e^{ix}+e^{-ix}\right)\quad\text{and}\quad\sin{x}=\frac{1}{2i}\left(e^{ix}-e^{-ix ...