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Tag
function
Recent questions tagged function
59
views
1
answers
What is a Lipschitz function and its significance?
What is a Lipschitz function and its significance?
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113k
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asked
Apr 8
Mathematics
lipschitz
function
significance
+
–
36
views
1
answers
Define and explain the concept of a limit of a function.
Define and explain the concept of a limit of a function.
MathsGee
Platinum
113k
points
MathsGee
asked
Apr 8
Mathematics
define
explain
concept
limit
function
+
–
67
views
1
answers
Solve Pascal equation as a function of y
Here is a Pascal equation that yields y as a function of theHighLowRange of the data over a number of days. Can you reverse theequation to yield the HighLowRange as a fu...
MathsGee
Platinum
113k
points
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asked
Mar 31
Mathematics
equation
differential
function
solution
+
–
69
views
1
answers
What is the conjugate of the complex number \(7+3i\) ?
What is the conjugate of the complex number \(7+3i\) ?
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 25
Mathematics
complex
real
equation
function
imaginary
conjugate
number
+
–
74
views
1
answers
What is a Bot?
What is a Bot?
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 15
Clothing Production
bot
automation
function
+
–
79
views
1
answers
To solve the maximization problem of the investor, we need to set up the Lagrangian and find the optimal conditions.
To solve the maximization problem of the investor, we need to set up the Lagrangian and find the optimal conditions. Let's consider the following problem:\[\underset{\lef...
Chefchef
105
points
Chefchef
asked
Mar 11
Mathematics
equation
calculus
solution
equations
function
+
–
116
views
1
answers
Given a sequence ${\{x_n\}_{n\in\mathbb{N}}}$ in a metric space X, prove the following statements:
Given a sequence ${\{x_n\}_{n\in\mathbb{N}}}$ in a metric space X, prove the following statements:(a) If $d(x_n,x_{n+1}) < 2^{-n}$ for every $n \in \mathbb{N}$, then ${\{...
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Platinum
113k
points
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asked
Mar 11
Mathematics
set
function
convex
closed
nonempty
compact
interior
+
–
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 $x \in X$...
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Platinum
113k
points
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asked
Mar 11
Mathematics
function
converge
prove
sum
infinite
telescoping
partial
+
–
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
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113k
points
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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...
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113k
points
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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...
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113k
points
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asked
Mar 10
Mathematics
prove
set
function
sequence
bounded
converge
open
+
–
170
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
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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
+
–
59
views
1
answers
Let $u$ be a harmonic function on a region $\Omega$. What can we say about the set of points such that . . .
Let $u$ be a harmonic function on a region $\Omega$. What can we say about the set of points such that $\nabla u = 0$, that is, the set of points where $u_x = u_y = 0$?
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
harmonic
function
region
points
+
–
136
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...
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Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
prove
zero
in
calculus
bounded
differentiable
function
+
–
68
views
1
answers
Compute $$\int_0^\infty \frac{dx}{1 + x^n}$$ for $n \geq 2$.
Compute$$\int_0^\infty \frac{dx}{1 + x^n}$$for $n \geq 2$.
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
sequence
real
proof
analysis
approximation
epsilon
function
+
–
88
views
1
answers
Suppose $f$ is an entire function, and that for every power series:
Suppose $f$ is an entire function, and that for every power series:$$ f(z) = \sum_{n=0}^\infty c_n (z - a)^n$$at least one coefficient is 0. Prove that $f$ is polynomial....
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
entire
function
power
series
+
–
69
views
1
answers
Let $f \in \mathcal{H}(\Omega)$. Under certain conditions on $z, \Gamma$, we have that:
Let $f \in \mathcal{H}(\Omega)$. Under certain conditions on $z, \Gamma$, we have that:$$ f^{(n)}(z) = \frac{n!}{2\pi i} \int_\Gamma \frac{f(\zeta)}{(\zeta - z)^{n+1}} d\...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
function
converge
generator
monte-carlo
number
simulation
random
+
–
60
views
1
answers
In what other discs can this be done?
There is a region $\Omega$ such that $\text{exp}(\Omega) = D(1,1)$. Show that the exponential function is one-to-one on $\Omega$, but that there are many such $\Omega$. F...
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Platinum
113k
points
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asked
Mar 10
Mathematics
exponential
function
disc
region
coefficients
+
–
66
views
1
answers
Prove that $f$ must be polynomial.
Suppose that $f$ is an entire function, and$$ | f(z) | \leq A + B|z|^k$$for all $z$, where $A, B, k$ are positive real numbers. Prove that $f$ must be polynomial.
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Platinum
113k
points
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asked
Mar 10
Mathematics
prove
theorem
math
sum
minimum
function
real
+
–
138
views
1
answers
Suppose $f, g$ are entire functions, and suppose that for all $z \in \mathbb{C}$, that $| f(z) | \leq | g(z)|$. What conclusion can you draw?
Suppose $f, g$ are entire functions, and suppose that for all $z \in \mathbb{C}$, that $| f(z) | \leq | g(z)|$. What conclusion can you draw?
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
function
real
numbers
complex
formula
approximation
estimate
+
–
100
views
1
answers
Suppose $x_1,...,x_n \in \mathbb{R}^D$ are data points, and we introduce an outlier $x^o$ with the property that . . .
Suppose $x_1,...,x_n \in \mathbb{R}^D$ are data points, and we introduce an outlier $x^o$ with the property that, for some $\delta 0$, $\Vert x_i - x^o \Vert_2 \delta$...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
set
real
function
vector
convex
open
convexity
+
–
72
views
1
answers
Let $x_1,...,x_n \in \mathbb{R}^d$. Fix some positive integer $K$.
Let $x_1,...,x_n \in \mathbb{R}^d$. Fix some positive integer $K$. Let $C_1,...,C_K$ be a partition of the data with centroids $\mu_1,...,\mu_K$. Let$$ F(C_1,...,C_k) \s...
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Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
real
set
function
vector
convex
open
convexity
+
–
161
views
1
answers
Let $x,y \in \mathbb{R}^{d \times 1}$. Prove that $xy^T \in \mathbb{R}^{d \times d}$ has at most rank 1.
Let $x,y \in \mathbb{R}^{d \times 1}$. Prove that $xy^T \in \mathbb{R}^{d \times d}$ has at most rank 1.
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
vector
space
product
function
fields
closed
orbit
+
–
65
views
1
answers
Recall that the variance of a set of numbers $x_1,...,x_n \in \mathbb{R}$ is defined as
Recall that the variance of a set of numbers $x_1,...,x_n \in \mathbb{R}$ is defined as $\sigma^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2$, where we define the mean as $...
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 10
Mathematics
function
set
vector
real
convex
open
convexity
+
–
112
views
1
answers
The function: \( v(t) = \frac{5}{2}t^{\frac{3}{2}}(7-t) - t^{\frac{5}{2}} \) Please find its derivative and show me the steps.
The function: \( v(t) = \frac{5}{2}t^{\frac{3}{2}}(7-t) - t^{\frac{5}{2}} \)Please find its derivative and show me the steps.
e.K2
134
points
e.K2
asked
Mar 7
Mathematics
derivative
steps
function
+
–
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
+
–
97
views
1
answers
The number of guests allocated to each wine waiter at a function where various drinks are to be served, is ... people.
The number of guests allocated to each wine waiter at a function where various drinks are to be served, is ... people.
MathsGee
Platinum
113k
points
MathsGee
asked
Mar 6
Hospitality & Tourism
guests
wine
waiter
function
drinks
served
+
–
111
views
1
answers
Solve
\( f l\left(x_{2}\right)=\frac{-2 c}{b-\sqrt{b^{2}-4 a c}}=\frac{-2.000}{62.10-62.06}=\frac{-2.000}{0.04000}=-50.00 \)
W.W3
104
points
W.W3
asked
Feb 29
Education & Development
equation
solution
function
+
–
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
+
–
116
views
1
answers
What does Euler's totient function \(\phi (n)\) represent?
What does Euler's totient function \(\phi (n)\) represent?
Edzai Zvobwo
Bronze Status
6.2k
points
Edzai Zvobwo
asked
Feb 23
Mathematics
euler
totient
function
represent
+
–
113
views
1
answers
\( \int \frac{x}{x^{2}+4 x+5} d x \)
\( \int \frac{x}{x^{2}+4 x+5} d x \)
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 17
Mathematics
integration
function
derivative
inflection
evaluate
graph
sketch
+
–
133
views
1
answers
\( \int_{0}^{\frac{\pi}{2}} \sqrt{ }(1+\sqrt{ } \sin x) d x \)
\( \int_{0}^{\frac{\pi}{2}} \sqrt{ }(1+\sqrt{ } \sin x) d x \)
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Platinum
113k
points
MathsGee
asked
Feb 17
Mathematics
function
equation
differential
initial-conditions
inverse
error
integration
+
–
144
views
1
answers
\( \begin{array}{l}200 \% \times 200 \%=? \\ \begin{array}{ll}\text { A. } 40 & \text { C. } 4 \\ \text { B. } 400 \% & \text { D. } 0.4 \%\end{array}\end{array} \)
\( \begin{array}{l}200 \% \times 200 \%=? \\ \begin{array}{ll}\text { A. } 40 & \text { C. } 4 \\ \text { B. } 400 \% & \text { D. } 0.4 \%\end{array}\end{array} \)
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 17
Mathematics
determinant
calculus
function
graph
domain
+
–
118
views
1
answers
If \( 2^{m+n}=32 \) and \( 3^{3 m-2 n}=243 \) find \( m: n= \) ?
if \( 2^{m+n}=32 \) and \( 3^{3 m-2 n}=243 \) find \( m: n= \) ?
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 17
Mathematics
function
set
real
equation
positive
calculate
solution
+
–
93
views
1
answers
Plot the constant, linear, quadratic, and cubic Taylor polynomials for \( \cos (x) \) computed at \( x_{0}=0 \) over the interval \( [a, b]= \) \( [-\pi / 2, \pi / 2] \). In each case, compute a bound on the remainder.
Plot the constant, linear, quadratic, and cubic Taylor polynomials for \( \cos (x) \) computed at \( x_{0}=0 \) over the interval \( [a, b]= \) \( [-\pi / 2, \pi / 2] \)....
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
polynomial
upper
bound
error
function
taylor
maximum
+
–
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...
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Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
function
prove
theorem
positive
bounded
integer
taylor
+
–
75
views
1
answers
Suppose that \( u \) is continuous on \( [a, b] \) and differentiable on \( (a, b) \). Then there is a point \( \xi \) in \( (a, b) \) such that \[ u(b)-u(a)=u^{\prime}(\xi)(b-a) \]
Suppose that \( u \) is continuous on \( [a, b] \) and differentiable on \( (a, b) \). Then there is a point \( \xi \) in \( (a, b) \) such that\[u(b)-u(a)=u^{\prime}(\xi...
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
function
integration
concave
inflection
graph
derivative
sketch
+
–
122
views
1
answers
Write down a definition for \( \lim _{x \rightarrow \bar{x}} u(x)=\infty \).
Write down a definition for \( \lim _{x \rightarrow \bar{x}} u(x)=\infty \).
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Platinum
113k
points
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Feb 16
Mathematics
write
down
definition
calculus
function
+
–
128
views
1
answers
Compute, if possible, the limits: \( \lim _{x \rightarrow 0} \sin (x) \) and \( \lim _{x \rightarrow 0} \sin (1 / x) \)
Compute, if possible, the limits: \( \lim _{x \rightarrow 0} \sin (x) \) and \( \lim _{x \rightarrow 0} \sin (1 / x) \)
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Platinum
113k
points
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asked
Feb 16
Mathematics
limits
calculus
function
calculate
logarithms
logs
exponents
+
–
85
views
2
answers
Solve the first-order linear differential equation \(\frac{dx}{ dy} +y=e ^x \)
Solve the first-order linear differential equation \(\frac{dx}{ dy} +y=e ^x \)
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Platinum
113k
points
MathsGee
asked
Feb 15
Mathematics
differential
equation
function
integral
constant
axes
curve
+
–
97
views
2
answers
Solve the separable differential equation \(\frac{dx}{ dy} =xy\).
Solve the separable differential equation \(\frac{dx}{ dy} =xy\).
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 15
Mathematics
differential
equation
function
integral
constant
axes
curve
+
–
98
views
1
answers
Use Newton’s Method to determine \(x_2\) for the given function \(f(x)=7x^3-8x+4, x_0=-1\)
Use Newton’s Method to determine \(x_2\) for the given function \(f(x)=7x^3-8x+4, x_0=-1\)
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 15
Mathematics
newton
method
determine
function
+
–
73
views
1
answers
Compute the differential of the given function \(u=t^2\cos{2t}\)
Compute the differential of the given function \(u=t^2\cos{2t}\)
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Platinum
113k
points
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Feb 15
Mathematics
compute
differential
function
+
–
93
views
1
answers
Compute the differential of the given function\( f(x)=3 x^{6}-8 x^{3}+x^{2}-9 x-4 \)
Compute the differential of the given function\( f(x)=3 x^{6}-8 x^{3}+x^{2}-9 x-4 \)
MathsGee
Platinum
113k
points
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asked
Feb 15
Mathematics
compute
differential
function
+
–
70
views
1
answers
Find the linear approximation to \( h(y)=\sin (y+1) \) at \( y=0 \). Use the linear approximation to approximate the value of \( \sin (2) \) and \( \sin (15) \). Compare the approximated values to the exact values.
Find the linear approximation to \( h(y)=\sin (y+1) \) at \( y=0 \). Use the linear approximation to approximate the value of \( \sin (2) \) and \( \sin (15) \). Compare ...
MathsGee
Platinum
113k
points
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asked
Feb 15
Mathematics
function
find
equation
approximation
determine
calculus
linear
+
–
79
views
1
answers
Find the linear approximation to \( h(y)=\sin (y+1) \) at \( y=0 \). Use the linear approximation to approximate the value of \( \sin (2) \) and \( \sin (15) \). Compare the approximated values to the exact values.
Find the linear approximation to \( h(y)=\sin (y+1) \) at \( y=0 \). Use the linear approximation to approximate the value of \( \sin (2) \) and \( \sin (15) \). Compare ...
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Platinum
113k
points
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asked
Feb 15
Mathematics
function
approximation
linear
calculus
determine
find
equation
+
–
91
views
1
answers
Find a linear approximation to the function \( g(t)=\mathbf{e}^{\sin (t)} \) at \( t=-4 \)
Find a linear approximation to the function \( g(t)=\mathbf{e}^{\sin (t)} \) at \( t=-4 \)
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Platinum
113k
points
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asked
Feb 15
Mathematics
linear
approximation
function
calculus
find
determine
equation
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–
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