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Home
Tag
prove
Recent questions tagged prove
72
views
1
answers
How do you identify which lines are parallel?
How do you identify which lines are parallel?
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 11
Mathematics
prove
mathematics
vector
parallel
line
product
point
+
–
135
views
1
answers
How can you prove that a diameter that is perpendicular to a chord bisects the chord and its arc?
How can you prove that a diameter that is perpendicular to a chord bisects the chord and its arc?
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 11
Mathematics
prove
diameter
perpendicular
chord
bisects
arc
+
–
84
views
1
answers
Prove that $x_n \rightarrow x$.
Assume ${\{x_n\}_{n\in\mathbb{N}}}$ is a Cauchy sequence in a metric space X, and there exists a subsequence ${\{x_{n_k}\}_{k\in\mathbb{N}}}$ that converges to $x \in X$...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 11
Mathematics
function
converge
prove
sum
infinite
telescoping
partial
+
–
65
views
1
answers
Prove B'ezout’s Theorem for Plane Curves
Prove Bezout's Theorem for Plane Curves
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 11
Mathematics
prove
bezout
theorem
plane
curves
+
–
102
views
1
answers
Prove that every meromorphic function on $S^2$ is rational.
Prove that every meromorphic function on $S^2$ is rational.
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
meromorphic
function
rational
+
–
106
views
1
answers
Let $L_1, L_2$ be lines in the plane. For which pairs of $L_1, L_2$ do there exists real functions,
Let $L_1, L_2$ be lines in the plane. For which pairs of $L_1, L_2$ do there exists real functions, harmonic on the entire plane, 0 on $L_1 \cup L_2$, but not vanishing i...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
function
real
prove
points
region
harmonic
sequence
+
–
82
views
1
answers
Show that $\{ u_n \}$ must be positive.
Let $\Omega$ be a region, $K$ a compact subset of $\Omega$, and fix some $z_0 \in \Omega$. Let $u$ be any positive harmonic function. Prove that there exists $\alpha, \be...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
function
positive
calculus
bounded
differentiable
zero
+
–
77
views
1
answers
Prove that $f_n$ converges uniformly on compact subsets of $\Omega$.
Let $\Omega$ be a region, and $f_n \in \mathcal{H}(\Omega)$ for all $n$. Set $u_n = \Re(f_n)$, and suppose $u_n$ converges uniformly on compact subsets of $\Omega$ and th...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
set
function
sequence
bounded
converge
open
+
–
169
views
1
answers
Prove that either $f, \overline{f}$ must be holomorphic on $\Omega$.
Suppose $f$ is a complex function on a region $\Omega$, and both $f, f^2$ are harmonic on $\Omega$. Prove that either $f, \overline{f}$ must be holomorphic on $\Omega$.
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
function
prove
calculus
differentiable
bounded
zero
+
–
93
views
1
answers
Let $u,v$ be real harmonic functions on a plane region $\Omega$. Under what conditions is $uv$ harmonic?
Let $u,v$ be real harmonic functions on a plane region $\Omega$. Under what conditions is $uv$ harmonic?Further, show that $u^2$ may not be harmonic on $\Omega$, unless $...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
function
points
region
harmonic
real
prove
sequence
+
–
135
views
1
answers
Prove that either $f$ has no zero in $\Omega$ or $f(z) = 0$ on all of $\Omega$.
Suppose $\Omega$ is a region, $f_n \in \mathcal{H}(\Omega)$ for $n \geq 1$. Suppose further that none of the $f_n$ has a zero in $\Omega$, and $f_n \to f$ uniformly on co...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
zero
in
calculus
bounded
differentiable
function
+
–
66
views
1
answers
Prove that $f$ must be polynomial.
Suppose that $f$ is an entire function, and$$ | f(z) | \leq A + B|z|^k$$for all $z$, where $A, B, k$ are positive real numbers. Prove that $f$ must be polynomial.
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
theorem
math
sum
minimum
function
real
+
–
58
views
1
answers
Show $L$ is not positive definite by proving $0$ is an eigenvalue of $L$.
Let $L = D - W \in \mathbb{R}^{n \times n}$ be the graph Laplacian for data with an associated symmetric weight matrix $W$, and $w_{ij} \in [0,1]$ for all $i,j = 1,...,n$...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
positive
definite
prove
product
inner
properties
matrix
+
–
75
views
1
answers
Prove that $F$ attains a minimum at $y = \frac{1}{n} \sum_{i=1}^n x_i$.
Let $\{ x_i \}_{i=1}^n \subset \mathbb{R}^D$. Define $F: \mathbb{R}^D \to [0,\infty)$ via:$$ F(y) = \sum_{i=1}^n \Vert x_i - y \Vert_2^2$$Prove that $F$ attains a minimum...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
minimum
sum
theorem
math
+
–
59
views
1
answers
Prove that $\langle x,y\rangle_M = x M y^T$ satisfies the properties of an inner product if $M$ is positive definite.
(a) Prove that $\langle x,y\rangle_M = x M y^T$ satisfies the properties of an inner product if $M$ is positive definite.(b) Show that $\langle x,y\rangle_M$ need not be ...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
properties
inner
product
positive
definite
+
–
59
views
1
answers
Prove that the Euclidean dot product . . .
Prove that the Euclidean dot product $\langle x, y \rangle = \sum_{i=1}^n x_i y_i, x, y \in \mathbb{R}^n$ is an inner product, where an inner product is a binary function...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
product
vectors
euclidean
inner
dot
two
prove
+
–
65
views
1
answers
Show that: $$\frac{\partial F}{\partial u} = 2\Sigma u$$
Let $\Sigma \in \mathbb{R}^{d \times d}$ be a symmetric matrix. Let $F: \mathbb{R}^d \to \mathbb{R}^d$ be the function $F(u) = u^T \Sigma u$ where $u$ is understood as a ...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
symmetric
matrix
vector
prove
+
–
75
views
1
answers
Prove that the empirical covariance matrix has rank $1$.
Suppose $(x_1, y_1), (x_2,y_2),...,(x_n,y_n) \in \mathbb{R}^2$ are sampled from a line $y = \alpha x$, for some $\alpha \in \mathbb{R}$. Prove that the empirical covarian...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
empirical
covariance
matrix
rank
+
–
72
views
1
answers
Prove that $\Vert \cdot \Vert_2$ is a norm.
Define the $l^2$ norm of $x \in \mathbb{R}^n$ to be$$ \Vert x \Vert_2 = \sqrt{ \sum_{i=1}^n | x_i |^2}$$Prove that $\Vert \cdot \Vert_2$ is a norm.
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
trigonometry
beta
alpha
identity
cosine
derive
+
–
82
views
1
answers
Prove that this operation is linear.
Recall that for a matrix $A = (A_{ij})_{i,j=1}^n \in \mathbb{R}^{n\times n}$, and a vector $x = (x_1,...,x_n)^T \in \mathbb{R}^{n \times 1}$, matrix-vector multiplication...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
matrix-vector
multiplication
prove
operation
linear
+
–
91
views
1
answers
Find (a) all horizontal and (b) all vertical asymptotes of the graph \[ y=\frac{|x| \sqrt{4 x^{4}+6 x^{2}+4}}{(2 x-1)^{2}(x+1)} \]
Find (a) all horizontal and (b) all vertical asymptotes of the graph\[y=\frac{|x| \sqrt{4 x^{4}+6 x^{2}+4}}{(2 x-1)^{2}(x+1)}\]
Ankit
105
points
Ankit
asked
Mar 6
Mathematics
function
domain
line
prove
theorem
rolle
assumption
+
–
126
views
1
answers
The solution of the inequality \(3(2-x) \geq 2(1-x)\) for real \(x\) is
(1) The solution of the inequality \( 3(2-x) \geq 2(1-x) \) for real \( x \) is
A.M9
111
points
A.M9
asked
Feb 26
Mathematics
prove
real
sequence
analysis
inequality
+
–
99
views
1
answers
Solution \( e^{i \pi}+1=0 \)
Solution \( e^{i \pi}+1=0 \)
S.A9
114
points
S.A9
asked
Feb 24
Mathematics
equation
prove
sequence
function
set
euler
+
–
94
views
1
answers
Explain \( e^{i \pi}+1=0 \)
Explain \( e^{i \pi}+1=0 \)
S.A9
114
points
S.A9
asked
Feb 24
Mathematics
equation
prove
sequence
euler
function
beautiful
set
+
–
145
views
1
answers
Prove the chain rule assuming \( u^{\prime} \) is continuous at \( v(x) \) and \( v \) is differentiable at \( x \). Hint: use the mean value theorem.
Prove the chain rule assuming \( u^{\prime} \) is continuous at \( v(x) \) and \( v \) is differentiable at \( x \). Hint: use the mean value theorem.
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
prove
chain
rule
continuous
differentiable
+
–
122
views
1
answers
Prove the mean value theorem by first reducing to the case \( u(a)=u(b)=0 \) and then using the fact that \( u(x) \) must take on a maximum or minimum value for some point \( \bar{x} \) in \( (a, b) \).
Prove the mean value theorem by first reducing to the case \( u(a)=u(b)=0 \) and then using the fact that \( u(x) \) must take on a maximum or minimum value for some poin...
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
function
prove
theorem
positive
bounded
integer
taylor
+
–
70
views
1
answers
Let \( \left\{f_{i}\right\} \) be a uniform Cauchy sequence consisting of uniformly continuous functions on a closed, bounded interval \( I \). Show that the limit is uniformly continuous.
Let \( \left\{f_{i}\right\} \) be a uniform Cauchy sequence consisting of uniformly continuous functions on a closed, bounded interval \( I \). Show that the limit is uni...
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
sequence
cauchy
triangle
inequality
set
prove
converge
+
–
129
views
1
answers
Show that for any \( 0<a<1 \) the sequence \( \left\{x^{i}\right\} \) converges uniformly to 0 on \( [0, a] \), but not for \( a=1 \).
Show that for any \( 0<a<1 \) the sequence \( \left\{x^{i}\right\} \) converges uniformly to 0 on \( [0, a] \), but not for \( a=1 \).
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
prove
converge
uniformly
sequence
set
construct
sequences
+
–
106
views
1
answers
Show that \( f(x)=1 / x \) is continuous but not uniformly continuous on \( (0,1) \).
Show that \( f(x)=1 / x \) is continuous but not uniformly continuous on \( (0,1) \).
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
continuous
uniformly
prove
+
–
81
views
1
answers
Evaluate \( e^{i \pi}+1=0 \)
Evaluate \( e^{i \pi}+1=0 \)
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 14
Ask Me Anything
equation
prove
sequence
+
–
95
views
1
answers
Prove that \( |x+y| \geq|x|-|y| \)
Prove that \( |x+y| \geq|x|-|y| \)
sashak299
105
points
sashak299
asked
Feb 9
Mathematics
prove
inequality
math
+
–
113
views
2
answers
Find the vertical and horizontal asymptotes of the graph of the function \( f(x)=\sqrt{x+1}-\sqrt{x} \).
Find the vertical and horizontal asymptotes of the graph of the function \( f(x)=\sqrt{x+1}-\sqrt{x} \).
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 7
Mathematics
function
domain
line
theorem
prove
rolle
assumption
+
–
158
views
2
answers
Find the vertical and horizontal asymptotes of the graph of the function \( f(x)=(2 x+3) / \sqrt{x^{2}-2 x-3} \).
Find the vertical and horizontal asymptotes of the graph of the function \( f(x)=(2 x+3) / \sqrt{x^{2}-2 x-3} \).
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 7
Mathematics
function
domain
line
theorem
prove
rolle
assumption
+
–
128
views
2
answers
Find any vertical and horizontal asymptotes of the graph of the function \( f(x)=(4 x-5) /(3 x+2) \).
Find any vertical and horizontal asymptotes of the graph of the function \( f(x)=(4 x-5) /(3 x+2) \).
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 7
Mathematics
function
domain
line
theorem
prove
rolle
assumption
+
–
155
views
1
answers
What will the next line in the pattern be? Show ALL your calculations.
Study the number pattern below:\(2 – 2 = 0\)\(2 – 1 = 1\)\(2 – 0 = 2\)What will the next line in the pattern be? Show ALL your calculations.
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 9
Mathematics
prove
calculations
series
grade12
convergent
+
–
157
views
1
answers
At your local store, you get 3 stickers for every R60 spent. 2.4.1 If you spend R480, how many stickers would you have? Show ALL your calculations.
At your local store, you get 3 stickers for every R60 spent. 2.4.1 If you spend R480, how many stickers would you have? Show ALL your calculations.
MathsGee
Platinum
113k
points
MathsGee
asked
Jan 9
Mathematics
prove
calculations
series
grade12
convergent
geometric
paper1
+
–
206
views
1
answers
How this equation come ? \(I_{1}(\alpha)=\frac{V}{\omega L}\left(1-\frac{2 \alpha}{\pi}-\frac{1}{\pi} \sin 2 \alpha\right)\)
\[I_{1}(\alpha)=a_{1} \cos \omega t+b_{1} \sin \omega t\]where \( b_{1}=0 \) because of the odd-wave symmetry, that is, \( f(x)=f(-x) \). Also, no even harmonics are gene...
s.i
108
points
s.i
asked
Dec 9, 2023
Mathematics
equation
solve
prove
+
–
136
views
1
answers
Which is the smallest?
Which is the smallest?(a) -1,(b) -1/2,(c) 0,(d) 3.
Edzai Zvobwo
Bronze Status
6.2k
points
Edzai Zvobwo
asked
Nov 20, 2023
Mathematics
smallest
integers
sum
prove
positive
numbers
+
–
276
views
1
answers
How do I show that all terms in a pattern are even?
How do I show that all terms in a pattern are even?
MathsGee
Platinum
113k
points
MathsGee
asked
Nov 14, 2023
Mathematics
sequence
sequences
prove
converge
+
–
148
views
1
answers
What is the sum of one and one?
What is the sum of one and one?
MathsGee
Platinum
113k
points
MathsGee
asked
Oct 10, 2023
Mathematics
prove
numbers
question
remainder
+
–
597
views
2
answers
Prove that \(n^2=(n+1)(n-1)+1\)
Prove that \(n^2=(n+1)(n-1)+1\)
MathsGee
Platinum
113k
points
MathsGee
asked
Jun 14, 2023
Mathematics
prove
real
function
sequence
set
vector
convexity
+
–
210
views
0
answers
What is this?
What is this? \( \Phi(\mathbf{r})=\Theta(\mathbf{r})-\Phi_{\mathrm{ref}}(\mathbf{r}) \)
MathsGee
Platinum
113k
points
MathsGee
asked
May 21, 2023
Mathematics
equation
mathematical
prove
math
calculate
logic
bank
+
–
233
views
1
answers
What does this maths equation say? \( e^{i \pi}+1=0 \)
What does this maths equation say? \( e^{i \pi}+1=0 \)
MathsGee
Platinum
113k
points
MathsGee
asked
May 15, 2023
Mathematics
equation
beautiful
euler
most
prove
+
–
517
views
1
answers
Prove that \(x^2+2 x y+2 y^2\) cannot be negative for \(x, y \in \mathrm{R}\).
Prove that \(x^2+2 x y+2 y^2\) cannot be negative for \(x, y \in \mathrm{R}\).
MathsGee
Platinum
113k
points
MathsGee
asked
May 14, 2023
Mathematics
calculus
proof
algebra
real-numbers
prove
function
set
+
–
322
views
1
answers
Explain \( e^{i \pi}+1=0 \)
Explain \( e^{i \pi}+1=0 \)
MathsGee
Platinum
113k
points
MathsGee
asked
May 14, 2023
Mathematics
equation
prove
sequence
euler
beautiful
+
–
358
views
1
answers
Simplify the binomial coefficients
(a) Simplify the difference of binomial coefficients\[\left(\begin{array}{l}n \\3\end{array}\right)-\left(\begin{array}{c}2 n \\2\end{array}\right) \text {, where } n \ge...
MathsGee
Platinum
113k
points
MathsGee
asked
May 13, 2023
Mathematics
binomial
coefficients
prove
satisfy
recursion
function
real
+
–
780
views
1
answers
How do you calculate the Bessel function of the second kind?
How do you calculate the Bessel function of the second kind? use latex
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 29, 2023
Mathematics
function
bessel
equation
differential
write
second-order
prove
+
–
769
views
2
answers
How do you calculate the Bessel function of the first kind?
How do you calculate the Bessel function of the first kind? Use latex
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 29, 2023
Mathematics
function
bessel
equation
differential
write
second-order
prove
+
–
322
views
1
answers
Where is Roodepoort?
Where is Roodepoort?
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 15, 2023
Climate & Environment
roodepoort
calculate
prove
markov
+
–
171
views
1
answers
Is \(\phi\) satisfiable?
Is \(\phi\) satisfiable?
Maths-Genie
Bronze Status
9.4k
points
Maths-Genie
asked
Mar 14, 2023
Mathematics
phi
prove
satisfiable
+
–
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