# Tagged Questions

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### Real Analysis Riemann integrals with piece wise function

this is part of my homework assignment and I have been stuck on it for a few days. Let f be the function on [0,1] given by f(x)= { 1 if x does not = 1/2 and 2 if x=1/2 Prove f is Riemann integrable ...
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### Finding Partition, Riemanns Integral

Define $f:[0,2]\rightarrow\mathbb{R}$ by setting $f(x)=1$ if $x\not=1$ and $f(1)=3$. Find a partition $D$ of $[0,2]$ for which $S_D-s_D<2^{-1000}$.
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### Prove $\int \limits_0^b x^3$ = $\frac{b^4}{4}$ by considering partitions [0, b] in $n$ equal subinvtervals.

Hi Guys I was given this question as an exercise in real analysis class. Here is what I came up with. Any help is appreciated! Prove $\int \limits_0^b x^3$ = $\frac{b^4}{4}$ by considering ...
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### integral partition, real analysis

I'm struggling with this question: If we have $f(x) = x^2$ and $P_n$ which partitions $[1,3]$ into $n$ sub-intervals, each equal in length,how can I write the formulas for $L(f,P_n)$ and $U(f,P_n)$ ...
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### Partitions of a closed interval on the reals

I'm currently trying to go through my textbook in real analysis where the integral is defined. And I'm really confused by something that seems very counter intuitive, and the proof isn't given, and so ...
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### Refinements and partitions

Suppose $P_1, ... P_n$ are finite partitions of the set $X$. Let $Q_n$ be the smallest common refinenement of the partitions $( P_i )$. I want to show that $Q_{n+1}$ is a refinement of $Q_n$. My ...
### Contructing a $\delta$-fine tagged partition from the old ones
Let $[a,b]\subset \mathbb{R}$. A tagged partition of $[a,b]$ is a set $D=\{(t_i,I_i)\}_{i=1}^m$ where $\{I_i\}_{i=1}^m$ is a partition of $[a,b]$ consisting of closed non-overlapping subintervals of ...