# Tagged Questions

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### Single Variable Calculus Reference Recommendations

This question is a generalization of the common question asking for calculus references. It is here to abstract away the repetition, and give a canonical resource for calculus references. I'm ...
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### Differentiation of $x^{\sqrt{x}}$, how?

The answer is (I think) $x^{\sqrt{x}-0.5} (1+0.5\ln(x))$, but how?
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### When are the limit operations commutative?

I'll come up with a question that has bothered me for a long period of time. The question seems relatively simple, but I personally didn't manage to find an answer to it. In many cases I met problems ...
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### $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$

(Fitzpatrick Advanced Calculus 2e, Sec. 2.4 #12) For $c \gt 0$, consider the quadratic equation $x^2 - x - c = 0, x > 0$. Define the sequence $\{x_n\}$ recursively by fixing $|x_1| \lt c$ and ...
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### Proof of an estimate for the tail of a normal distribution

My advisor told me to look up the proof of the following standard estimate so that we can adapt it to the case where we are dealing with something similar but including the addition of a polynomial ...
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### Finding the limit of $\frac{Q(n)}{P(n)}$ where $Q,P$ are polynomials

Suppose that $$Q(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}$$and $$P(x)=b_{m}x^{m}+b_{m-1}x^{m-1}+\cdots+b_{1}x+b_{0}.$$ How do I find $$\lim_{x\rightarrow\infty}\frac{Q(x)}{P(x)}$$ and what ...
### Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?
Can someone give a simple explanation for why the harmonic series $$\sum_{n=1}^\infty\frac1n=\frac 1 1 + \frac 12 + \frac 13 + \cdots$$ doesn't converge, but it just grows very slowly? I'd ...