Question

Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

score 63 · Answer 1 · 2026-04-06 11:28:30

63

Views

Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

Published on 06 Apr 2026 - 11:28

score 112 · Answer 2 · 2026-03-25 04:43:41

112

Views

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score 73 · Answer 3 · 2026-04-04 00:28:48

73

Views

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38

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602

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79

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score 85 · Answer 13 · 2026-03-25 04:43:57

85

Views

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126

Views

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score 34 · Answer 15 · 2026-03-25 05:04:00

34

Views

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List Question

Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

Functions $f: \mathbb{R}^n \to \mathbb{R}$ such that $|f(x) -f(y)| \le C \prod_{i=1}^n |x_i - y_i|^{\alpha_i}$

Convergence of sequence of functions to x^2

Is it true that $\lim_{u\to 0}f\big(u,g(u)\big)=0$

Show $C^k([a,b])$ is a Banach space

Applications of Apostol Mathematical Analysis Theorem 1.1

Embedding and diffeomorphisms

A metric space with sufficient points(dense enough)

Can I approximate a unit vector in $C^d$ with complex algebraic vectors in the unit ball in $C^d$?

Bump function inequality

Give a countable set of periodic points of $T$ where $\Bbb T=[0,1)/\{0=1\}$

$\lim_{n \rightarrow \infty}\int_0^1f_n(x)$

Proving $ f:(0,1)\to R$ is uniformly continuous, where$ f(x)=1/(x+4)$ for all $x \in (0,1)$

Puzzled for a (supposed) way to show that $\det(e^A)=e^{{\rm tr}(A)}$

continuity after taking partial derivative

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