# Tagged Questions

Homework questions are welcome as long as they are asked honestly, explain the problem, and show sufficient effort. Please do not use this as the only tag for a question. For the answers on homework questions, helpful hints or instructions are preferred to a complete solution. Please do not add ...

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### A problem from Courant and John's volume 1, chapter 1

Let $a_n$ be a given sequence such that the sequence $b_n = pa_n + qa_{n + 1}$ where $|p| < q$, is convergent. Prove that $a_n$ converges. If $|p| > q > 0$, show that $a_n$ need not converge. ...
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### Simple question on integral

why: $$\int_0^1\int_{u(t)}^{u(t)+w(t)} f(t,v(t)) dv dt = \int_0^1 f(t,u(t)+\theta w(t))w(t) dt; ~~\theta\in[0,1]$$ how to get this ? Please help me Thank you.
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### Compact and non-compact curves in the plane

I want to find compact and non-compact curves in the plane: MY attempt" Suppose $f: \mathbb{R} \to \mathbb{R}$ is continous function. Put $C = \{ (x, f(x) ) \}$. Then $C$ is closed. IS it bounded? ...
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### Allocating observations to test whether two expected values are equal$\mu_{1}-\mu_{2}=\Delta\neq 0?$

Question: Suppose that you wish to test the hypothesis $H_{0}:\mu_{1}=\mu_{2}$ versus $H_{1}:\mu_{1}\neq \mu_{2}$,where both variances $\sigma^2_{1}$ and $\sigma^2_{2}$ are know ,A tatal of ...