Tagged Questions

Questions on the evaluation of limits.

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Prove that $\limsup\left(b_{n}a_{n}\right)=\limsup\left(a_{n}\right)$ when $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$

I'm having trouble with this homework question: "Let there be a sequence $\left(b_{n}\right)_{n=1}^{\infty}$ such that $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$. Let there also be some ...
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evaluating a complex limit to the power of one third [on hold]

Evaluate lim as $x$ approaches $\infty,$ $\displaystyle[(x^3+x^2)^\frac13 - (x^3-x^2)^\frac13$.
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How do you simplify this expression?

$$\lim_{h\to0}(\frac{x}{h(x+h+1)} + \frac{1}{x+h+1} - \frac{x}{h(x+1)})$$ I know the answer is $$\frac{1}{(1+x)^2}$$ But I can't get there
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Stuck on Infinite L'hopitals

I have been trying forever to figure out this problem, but I seem to get stuck in an infinite L'hopitals loop. See the question below: Find the value of the positive constant c such that: ...
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I need some basic introduction to limits

So, I know you can obviously cut out a value if it is multiplying and dividing something at the same time, right? Like: $$\frac{4h-2xh-h^2}{h} = \frac{h(4-2x-h)}{h} = 4-2x-h$$ But then I saw this ...
Prove: $\sum {{a_{{n_k}}}} < \infty \Rightarrow \sum {|{a_n}| < \infty }$
Prove: $$\sum {{a_{{n_k}}}} < \infty \Rightarrow \sum {|{a_n}| < \infty }$$ In words, if every sub-series of $\sum a_n$ converges then $\sum a_n$ converges absolutely. I know that: ...