User Vince Vickler - Mathematics Stack Exchange

9 votes

2 answers

554 views

Are there reasons to prefer one definition of the exponential function over the other?

asked Jan 3, 2023 at 22:48

6 votes

3 answers

789 views

Where is the mistake in the argument in favor of the (erroneous) claim "every Dedekind cut is a rational cut"?

asked May 10 at 16:52

5 votes

1 answer

108 views

Equation of the parabola $y=x^2$ sliding normally on the ellipse $x^2/6^2+y^2/3^2=1$, and opening outwards. How to avoid the use of $\text{sgn}(x)$?

asked Oct 23, 2022 at 8:46

4 votes

0 answers

85 views

How do we know that the derivative number is actually the slope of the tangent line ( to the graph of a given function)?

asked Jul 30, 2023 at 16:18

4 votes

3 answers

265 views

Without calculus, what is the maximum value of the rational function : $f(t)= \frac {30t} {t^2 + 2}$

asked Dec 4, 2022 at 0:37

3 votes

2 answers

78 views

Showing that the rational function $f(x)= \frac {x+1} {x^2 +3}$ behaves like $y= \frac 13 x +\frac 13$ around $x=0$

asked Dec 5, 2022 at 14:28

3 votes

0 answers

87 views

Is a series (an infinite series) a sequence or a limit?

asked Nov 9, 2022 at 20:54

3 votes

2 answers

159 views

Why does this formula yield a clockwise rotation for curves defined by a cartesian equation, and a counterclockwise rotation in parametric form?

asked Oct 13, 2022 at 15:34

3 votes

2 answers

153 views

$\sqrt {x^2} = |x|$ : how to relate $\sqrt {x^2}$ to the concept of "distance to $x$ from $0$"?

asked Jun 6, 2022 at 21:02

3 votes

1 answer

50 views

Making a coordinate system slide around a parabola in order to ( hopefully) make a parabola slide on its fixed coordinate system.

asked Jul 9, 2022 at 9:52

3 votes

1 answer

93 views

How to factor $ ab(x^2 +y^2) + xy (a^2 +b^2)$?

asked Nov 13, 2021 at 13:05

3 votes

2 answers

302 views

Two parallel lines with varying slopes and constant distance ( say 4 units) between them.

asked Nov 20, 2021 at 7:55

3 votes

2 answers

128 views

Is there a general method to operate the reduction of a rational expression to a sum : $\frac {1+2x}{1-3x} \rightarrow 1+5x+\frac{15x^3}{1-3x}$

asked Dec 9, 2021 at 22:06

3 votes

2 answers

44 views

How do 3 fractions having respectively $(a-x)^2$ , $(a+x)^2$ and $(a-x)$ as denominators add up to a fraction having $(a^2 - x^2)^2$ as denominator?

asked Dec 4, 2021 at 22:45

3 votes

2 answers

93 views

A question regarding the point-slope formula : does the formula really hold for any point of the straight line?

asked May 4, 2022 at 13:42

2 votes

1 answer

280 views

How to graph the elasticity function ( knowing the - linear-demand function and the price function )? What goes wrong in my Desmos graph?

asked Apr 26, 2022 at 9:28

2 votes

1 answer

85 views

If the number $\int_a^b f(x)dx$ exists, can I assert that there is some function $F$ such that $F(x)=\int_a^x f(t)dt$

asked Jan 18, 2022 at 10:54

2 votes

1 answer

33 views

A question regarding the conditions imposed on an index in the course of the proof of Sylow's theorem I.

asked Jan 4, 2022 at 19:49

2 votes

1 answer

75 views

Confusion about the last step of this proof of " Every subgroup of a cyclic group is cyclic":does not subcase $2.2$ contradict the desired conclusion

asked Jan 9, 2022 at 12:20

2 votes

0 answers

299 views

Are there applications of partial fraction decomposition ( of a rational function) outside integration problems?

asked Dec 6, 2021 at 18:10

2 votes

4 answers

199 views

Applying " divide by highest denominator power" to $ f(x)= \frac {4x+1} {\sqrt{x^2+9}}$ ( Context : limits at infinity and asymptotes).

asked Dec 13, 2021 at 22:46

2 votes

1 answer

56 views

How to derive easily : $|\sqrt{x+3} -2|=\frac {|x-1|}{\sqrt{x+3}+2}$? ( Context : a limit problem).

asked Nov 11, 2021 at 19:38

2 votes

1 answer

186 views

The determinant of a matrix is "linear in the rows "

asked Aug 18, 2022 at 20:46

2 votes

2 answers

74 views

Determining the cartesian equation of an ellipse ( be it neither in standard position nor orientation) given center, one vertex and one semi -axis

asked Oct 27, 2022 at 22:03

2 votes

2 answers

66 views

Geometrically ( vs. algebraically or analytically) how to predict the minimum of the product of two linear functions ( say, having the same slope)?

asked Dec 7, 2022 at 19:37

2 votes

0 answers

93 views

Determining the equation of a rational function from its given 3 branches graph

asked Dec 7, 2022 at 21:44

1 vote

1 answer

331 views

How to prove that : the graph of function $f$ is symmetric w.r.t. point $I=(a,b)$ iff $ f(2a-x)+f(x)= 2b$.

asked Dec 19, 2022 at 23:29

1 vote

1 answer

102 views

Proof of a Thm. required for Descartes' Rule Of signs : if $r\gt0, f(r)= 0$ , $f(x)= (x-r)Q(x)$ and $Q(x)$ has less variation in sign than $f(x)$

asked Dec 21, 2022 at 23:54

1 vote

1 answer

228 views

Derivation of Euler-Lagrange's equation by Susskind : " the change in x_i when I change v_i a little bit is $1/ \epsilon (= 1/ \Delta t)$".

asked Aug 15, 2023 at 22:19

1 vote

2 answers

33 views

How to recover the cartesian equation of a rotated parabola from its parametric equation obtained using linear algebra ( rotation matrix)?

asked Sep 1, 2023 at 19:51

Stack Exchange Network

88 Questions

Are there reasons to prefer one definition of the exponential function over the other?

Where is the mistake in the argument in favor of the (erroneous) claim "every Dedekind cut is a rational cut"?

Equation of the parabola $y=x^2$ sliding normally on the ellipse $x^2/6^2+y^2/3^2=1$, and opening outwards. How to avoid the use of $\text{sgn}(x)$?

How do we know that the derivative number is actually the slope of the tangent line ( to the graph of a given function)?

Without calculus, what is the maximum value of the rational function : $f(t)= \frac {30t} {t^2 + 2}$

Showing that the rational function $f(x)= \frac {x+1} {x^2 +3}$ behaves like $y= \frac 13 x +\frac 13$ around $x=0$

Is a series (an infinite series) a sequence or a limit?

Why does this formula yield a clockwise rotation for curves defined by a cartesian equation, and a counterclockwise rotation in parametric form?

$\sqrt {x^2} = |x|$ : how to relate $\sqrt {x^2}$ to the concept of "distance to $x$ from $0$"?

Making a coordinate system slide around a parabola in order to ( hopefully) make a parabola slide on its fixed coordinate system.

How to factor $ ab(x^2 +y^2) + xy (a^2 +b^2)$?

Two parallel lines with varying slopes and constant distance ( say 4 units) between them.

Is there a general method to operate the reduction of a rational expression to a sum : $\frac {1+2x}{1-3x} \rightarrow 1+5x+\frac{15x^3}{1-3x}$

How do 3 fractions having respectively $(a-x)^2$ , $(a+x)^2$ and $(a-x)$ as denominators add up to a fraction having $(a^2 - x^2)^2$ as denominator?

A question regarding the point-slope formula : does the formula really hold for any point of the straight line?

How to graph the elasticity function ( knowing the - linear-demand function and the price function )? What goes wrong in my Desmos graph?

If the number $\int_a^b f(x)dx$ exists, can I assert that there is some function $F$ such that $F(x)=\int_a^x f(t)dt$

A question regarding the conditions imposed on an index in the course of the proof of Sylow's theorem I.

Confusion about the last step of this proof of " Every subgroup of a cyclic group is cyclic":does not subcase $2.2$ contradict the desired conclusion

Are there applications of partial fraction decomposition ( of a rational function) outside integration problems?

Applying " divide by highest denominator power" to $ f(x)= \frac {4x+1} {\sqrt{x^2+9}}$ ( Context : limits at infinity and asymptotes).

How to derive easily : $|\sqrt{x+3} -2|=\frac {|x-1|}{\sqrt{x+3}+2}$? ( Context : a limit problem).

The determinant of a matrix is "linear in the rows "

Determining the cartesian equation of an ellipse ( be it neither in standard position nor orientation) given center, one vertex and one semi -axis

Geometrically ( vs. algebraically or analytically) how to predict the minimum of the product of two linear functions ( say, having the same slope)?

Determining the equation of a rational function from its given 3 branches graph

How to prove that : the graph of function $f$ is symmetric w.r.t. point $I=(a,b)$ iff $ f(2a-x)+f(x)= 2b$.

Proof of a Thm. required for Descartes' Rule Of signs : if $r\gt0, f(r)= 0$ , $f(x)= (x-r)Q(x)$ and $Q(x)$ has less variation in sign than $f(x)$

Derivation of Euler-Lagrange's equation by Susskind : " the change in x_i when I change v_i a little bit is $1/ \epsilon (= 1/ \Delta t)$".

How to recover the cartesian equation of a rotated parabola from its parametric equation obtained using linear algebra ( rotation matrix)?