# Recent questions tagged function

59
views
What is a Lipschitz function and its significance?
36
views
Define and explain the concept of a limit of a function.
67
views
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...
69
views
What is the conjugate of the complex number $$7+3i$$ ?
74
views
What is a Bot?
79
views
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... 116 views 1 answers 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 {\{... 84 views 1 answers 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... 102 views 1 answers Prove that every meromorphic function on S^2 is 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, harmonic on the entire plane, 0 on L_1 \cup L_2, but not vanishing i... 82 views 1 answers 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... 77 views 1 answers 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... 170 views 1 answers 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. 93 views 1 answers 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 ... 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 \nabla u = 0, that is, the set of points where u_x = u_y = 0? 136 views 1 answers 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... 68 views 1 answers Compute\int_0^\infty \frac{dx}{1 + x^n}for n \geq 2. 88 views 1 answers Suppose f is an entire function, and that for every power series: f(z) = \sum_{n=0}^\infty c_n (z - a)^nat least one coefficient is 0. Prove that f is polynomial.... 69 views 1 answers 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\... 60 views 1 answers 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... 66 views 1 answers Suppose that f is an entire function, and | f(z) | \leq A + B|z|^kfor all z, where A, B, k are positive real numbers. Prove that f must be polynomial. 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? 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, for some \delta 0, \Vert x_i - x^o \Vert_2 \delta... 72 views 1 answers 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... 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. 65 views 1 answers 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 ... 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. 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)}$
97
views
The number of guests allocated to each wine waiter at a function where various drinks are to be served, is ... people.
111
views
$$f l\left(x_{2}\right)=\frac{-2 c}{b-\sqrt{b^{2}-4 a c}}=\frac{-2.000}{62.10-62.06}=\frac{-2.000}{0.04000}=-50.00$$
99
views
Solution $$e^{i \pi}+1=0$$
94
views
Explain $$e^{i \pi}+1=0$$
116
views
What does Euler's totient function $$\phi (n)$$ represent?
113
views
$$\int \frac{x}{x^{2}+4 x+5} d x$$
133
views
$$\int_{0}^{\frac{\pi}{2}} \sqrt{ }(1+\sqrt{ } \sin x) d x$$
144
views
$$\begin{array}{l}200 \% \times 200 \%=? \\ \begin{array}{ll}\text { A. } 40 & \text { C. } 4 \\ \text { B. } 400 \% & \text { D. } 0.4 \%\end{array}\end{array}$$
118
views
if $$2^{m+n}=32$$ and $$3^{3 m-2 n}=243$$ find $$m: n=$$ ?
93
views
Plot the constant, linear, quadratic, and cubic Taylor polynomials for $$\cos (x)$$ computed at $$x_{0}=0$$ over the interval $$[a, b]=$$ $$[-\pi / 2, \pi / 2]$$....
122
views
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...
75
views
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...
122
views
Write down a definition for $$\lim _{x \rightarrow \bar{x}} u(x)=\infty$$.
128
views
Compute, if possible, the limits: $$\lim _{x \rightarrow 0} \sin (x)$$ and $$\lim _{x \rightarrow 0} \sin (1 / x)$$
85
views
Solve the first-order linear differential equation $$\frac{dx}{ dy} ​ +y=e ^x$$
97
views
Solve the separable differential equation $$\frac{dx}{ dy} ​ =xy$$.
98
views
Use Newton’s Method to determine $$x_2$$ for the given function $$f(x)=7x^3-8x+4, x_0=-1$$
73
views
Compute the differential of the given function $$u=t^2\cos{2t}$$
93
views
Compute the differential of the given function$$f(x)=3 x^{6}-8 x^{3}+x^{2}-9 x-4$$
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 ...
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 ...
Find a linear approximation to the function $$g(t)=\mathbf{e}^{\sin (t)}$$ at $$t=-4$$