User Vincenzo Tibullo - Mathematics Stack Exchange

40 votes

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Dimensions of symmetric and skew-symmetric matrices

answered Aug 23, 2012 at 10:10

28 votes

Why is $y=1/x$ a continuous function but not $y=(1/x)^2$?

answered Jun 8, 2017 at 7:40

15 votes

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Eigenvalues in terms of trace and determinant for matrices larger than 2 X 2

answered May 23, 2014 at 22:05

14 votes

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Derivative of $x^x$ at $x=1$ from first principles

answered Aug 1, 2012 at 21:24

11 votes

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Consecutive Prime Gap Sum (Amateur)

answered Aug 14, 2014 at 1:02

11 votes

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Algebraic Manipulation with Cube Roots

answered Sep 6, 2020 at 19:35

10 votes

Looking for simple function: Passes through 0, sqrt like but never reaches 100

answered Oct 4, 2012 at 16:51

9 votes

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What does distance of a point from line being negative signify?

answered Jul 24, 2020 at 5:57

8 votes

How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?

answered Aug 19, 2012 at 10:36

8 votes

How to calculate ratio of areas of the shaded triangle and the hexagon?

answered Sep 15, 2012 at 16:22

8 votes

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Drawing an arrow

answered Jun 6, 2015 at 2:31

8 votes

Calculating $\frac{1.01^5}{1.01^5-1}$ without calculator with good accuracy?

answered Dec 24, 2022 at 11:40

6 votes

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Formula for the tangent to an ellipse at a given point (splitting formula)

answered Feb 26, 2023 at 20:58

6 votes

The antiderivative of $\cos^5(x)\sin^5(x)$ - is this incorrect?

answered May 18, 2014 at 22:41

6 votes

Why don't we draw modulus bars when we open 'under root' in indefinite integration?

answered Jul 29, 2020 at 13:24

6 votes

Curious inequality: $(1+a)(1+a+b)\geq\sqrt{27ab}$

answered May 8, 2016 at 18:44

5 votes

Show that: $\nabla \times (\phi F) = \nabla \phi \times F + \phi \nabla \times F$

answered Apr 30, 2017 at 11:16

5 votes

$2n$th derivative of $(x^2-1)^n$

answered Aug 20, 2020 at 7:23

5 votes

How to factor $x^6+x^5-3\,x^4+2\,x^3+3\,x^2+x-1$ by hand?

answered Jan 2, 2016 at 18:38

5 votes

Showing $ \int_0^{2 \pi } \frac{dt}{a^2 \cos^2 t + b^2 \sin^2 t} = \frac{2 \pi}{ab}$

answered Jun 3, 2015 at 20:25

5 votes

Computing a limit similar to the exponential function

answered May 14, 2015 at 21:17

5 votes

Chebyshev polynomial properties

answered Sep 10, 2012 at 15:10

5 votes

Accepted

Equation of the locus of centre of the ellipse?

answered Aug 1, 2012 at 20:49

5 votes

Accepted

Finding $a$ from $\lim\limits_{x\rightarrow0}(1+a\sin x)^{\csc x} =4$

answered Jul 29, 2012 at 16:06

5 votes

Taking derivatives in index notation

answered Sep 16, 2012 at 17:14

5 votes

Inside a limit, when can you substitute terms?

answered Jan 21, 2023 at 19:23

5 votes

Real roots of $x^7+5x^5+x^3−3x^2+3x−7=0$?

answered Sep 18, 2020 at 7:32

5 votes

Accepted

Calculate the limit of $\frac{\cos x}{(1+\sin x)e^x}$

answered Apr 12, 2023 at 19:20

4 votes

How to find $\text{lim}_{x \to 1} \dfrac{\sqrt{x} -1}{\sqrt{2x +3} - \sqrt{5}} $

answered Apr 3, 2023 at 19:31

4 votes

Accepted

Showing a bound of the second derivative using remainder in integral form

answered Jan 21, 2023 at 20:51

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393 Answers

Dimensions of symmetric and skew-symmetric matrices

Why is $y=1/x$ a continuous function but not $y=(1/x)^2$?

Eigenvalues in terms of trace and determinant for matrices larger than 2 X 2

Derivative of $x^x$ at $x=1$ from first principles

Consecutive Prime Gap Sum (Amateur)

Algebraic Manipulation with Cube Roots

Looking for simple function: Passes through 0, sqrt like but never reaches 100

What does distance of a point from line being negative signify?

How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?

How to calculate ratio of areas of the shaded triangle and the hexagon?

Drawing an arrow

Calculating $\frac{1.01^5}{1.01^5-1}$ without calculator with good accuracy?

Formula for the tangent to an ellipse at a given point (splitting formula)

The antiderivative of $\cos^5(x)\sin^5(x)$ - is this incorrect?

Why don't we draw modulus bars when we open 'under root' in indefinite integration?

Curious inequality: $(1+a)(1+a+b)\geq\sqrt{27ab}$

Show that: $\nabla \times (\phi F) = \nabla \phi \times F + \phi \nabla \times F$

$2n$th derivative of $(x^2-1)^n$

How to factor $x^6+x^5-3\,x^4+2\,x^3+3\,x^2+x-1$ by hand?

Showing $ \int_0^{2 \pi } \frac{dt}{a^2 \cos^2 t + b^2 \sin^2 t} = \frac{2 \pi}{ab}$

Computing a limit similar to the exponential function

Chebyshev polynomial properties

Equation of the locus of centre of the ellipse?

Finding $a$ from $\lim\limits_{x\rightarrow0}(1+a\sin x)^{\csc x} =4$

Taking derivatives in index notation

Inside a limit, when can you substitute terms?

Real roots of $x^7+5x^5+x^3−3x^2+3x−7=0$?

Calculate the limit of $\frac{\cos x}{(1+\sin x)e^x}$

How to find $\text{lim}_{x \to 1} \dfrac{\sqrt{x} -1}{\sqrt{2x +3} - \sqrt{5}} $

Showing a bound of the second derivative using remainder in integral form