# Tagged Questions

Questions on the evaluation of limits.

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### Exchanging the limit and Lebesgue integral for every set in the measure space

Let $(X,\mathcal{M},\mu)$ be a measure space and let a sequence of $\mathcal{M}$-measurable functions $\{f\}_k$, where $f_k: X\rightarrow [0,\infty]$. Assume that $f_k\rightarrow f$ pointwise and ...
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### Problem finding limit - which function is asymptotically larger

I have a homework question, so please don't answer fully but I would appreciate a push in the right direction. Basically we need to figure out if $n^{n+\frac{1}{2}}e^{-n}$ is larger,smaller, or equal ...
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### A simpler solution to a limit question?

Okay I saw this limit question in Thomas' Calculus 12th Edition: $\lim \limits_{x \to 0} \frac{\tan3x}{\sin8x}$ The answer is $\frac{3}{8}$. I was able to get the correct answer using this ...
for $a>1$: $$\mathop {\lim }\limits_{x \to \infty } \frac{{{a^x}}}{x} = \infty$$ So, by the definition of Cauchy for limits, for any $M>0$ I need to find a $D>0$ such that: $x>D$ ...