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$how to find derivative of $x^2\sin(x)$ using only the limit definition of a derivative$

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how to find derivative of $x^2\sin(x)$ using only the limit definition of a derivative

I'm trying to find the derivative of $x^2\sin x$ using only the limit definition of a derivative. I've tried two approaches, one using the diffe...

Published: Aug 10, 2026

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Minimal axioms for a group

My group theory is very rusty. If I want to just start with left inverses and left identities, must I link the axioms, or can I leave them independent? e....

Published: Aug 10, 2026

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What exactly is a random variable?

I don't really understand the definition of a random variable. I also find the Wikipedia entry on random variables kind of confusing. Can someone giv...

Published: Aug 10, 2026

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Why Zero divided by Zero is undefined and not Infinity [duplicate]

apologize in advance if this is a duplicate, but I found a lot questions related to this but none answering this specific question. My logic is: let'...

Published: Aug 10, 2026

general

How to denote a set of sequences?

How do you denote a set of sequences of a certain length, consisting of real numbers? For example, is this correct? $$S=\{A:A=\{a_k\}_{k=1}^{10}\wedge (\f...

Published: Aug 10, 2026

general

How do I express 108 as the product of powers of its prime factors?

How do I express $108$ as the product of powers of its prime factors? I've got $2^2 \times 3^3$ is this correct?

Published: Aug 10, 2026

updates

What means a "$\setminus$" logic symbol?

I have a task to calculate a double integral on a region $D=A\setminus B$, where $A=\{(x,y): \text{some system of inequalities}\}, B= \{(x,y): \text{anoth...

Published: Aug 10, 2026

general

What is the volume of an ellipsoid? [closed]

How to use integrals to find the volume of the following ellipsoid? What are the associated parametric equations for this sort of ellipsoid?

Published: Aug 10, 2026

$Lipschitz Continuous $\Rightarrow$ Uniformly Continuous$

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Lipschitz Continuous $\Rightarrow$ Uniformly Continuous

The Question: Prove that if a function $f$ defined on $S \subseteq \mathbb R$ is Lipschitz continuous then $f$ is uniformly continuous on $S$. Definition....

Published: Aug 10, 2026

general

Does the perimeter of a semicircle include the diameter? [closed]

Is the perimeter of a semicircle $(\pi)(\text{radius})$ or $(\pi)(\text{radius})+\text{diameter}$?

Published: Aug 10, 2026

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