# Questions tagged [riemann-sum]

This tag is for questions about Riemann sums and Darboux sums.

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### Riemann Sum Problem Explanation f(x)=mx on left endpoints using xk

I am learning Riemann when I encountered this question and its solution. Question A curve f(x)=mx in closed interval [a,b] where m>0 and a>=0. Calculate riemann sum of f(x) using xk as left ...
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### Using Riemann sums to approximate the second antiderivative

I’m currently working on a coding project where I’m given the the net force acting on an object at any time $t$ (meaning I essentially have its acceleration). I know the object’s current position and ...
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### Converting Riemann Sum to Definite Integral with Unequal $\Delta x$ Values

How can I convert this Riemann sum to a definite integral? $$\lim_\limits{n\to\infty}\sum_{i=1}^n\pi\biggl(1.6875+\frac{.75775i}{n}\biggl)^2\frac{1.625}{n}$$ I'm confused because the usual definition ...
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### Let $a_n$ be a series and $n_k$ be a Permutation, Prove that if $\lim_{n\rightarrow \infty}a_n = a$ ifff $\lim_{k\rightarrow \infty}a_{n_k} = a$ [closed]

Let $a_n$ be a series and $n_k$ be a Permutation, Prove that if $\lim_{n\rightarrow \infty}a_n = a$ if and only if $\lim_{k\rightarrow \infty}a_{n_k} = a$ At first, looking is really "looks like&...
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### do the upper and lower darboux sums of a function change depending on the norm(mesh) of the partition?

if we have two partitions of the interval [0,1] p1 and p2 so that the norm of p1 is greater than the norm of p2, then does that mean that U(f,p1) > U(f,p2) ?
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### $\lim_{n \to \infty} {\frac{1}{n^2}\sum_{k=0}^{n}{\frac{1}{\ln{(1 + \frac{(n+k)\sqrt{n^2+k^2}}{n^3})}}}}$

How can I solve $$\lim_{n \to \infty} {\frac{1}{n^2}\sum_{k=0}^{n}{\frac{1}{\ln{(1 + \frac{(n+k)\sqrt{n^2+k^2}}{n^3})}}}}$$ It looks like a Riemann limit to me, but I'm not able to get it to a final ...
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### The Riemann integral of a non-negative function

Suppose $g : [−1,1] \to\mathbb R$ is Riemann integrable on $[−1,1], g(x) ≥ 0$ for all $x ∈ [−1,1]$, and $g(0) > 0$. Does it follow that $\int_{-1}^{1} g > 0$? I tried proving that it is true by ...
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