Given $$f(x,y) = x^2-3xy+5,$$ where $$R : |x-2| \leq 0.1, \ |y-1| \leq 0.1$$ Now, this function is approximated by a polynomial $$L(x,y) = x-6y+7$$ at the point $(2,1)$.
How to find out the maximum value of an absolute error in $R$?
2026-03-27 02:34:25.1774578865
How to find out the maximum value of absolute error?
443 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in MAXIMA-MINIMA
- optimization with strict inequality of variables
- Minimum value of a complex expression involving cube root of a unity
- Calculation of distance of a point from a curve
- Find all local maxima and minima of $x^2+y^2$ subject to the constraint $x^2+2y=6$. Does $x^2+y^2$ have a global max/min on the same constraint?
- Solving discrete recursion equations with min in the equation
- Trouble finding local extrema of a two variable function
- Why do I need boundedness for a a closed subset of $\mathbb{R}$ to have a maximum?
- Find the extreme points of the function $g(x):=(x^4-2x^2+2)^{1/2}, x∈[-0.5,2]$
- Maximizing triangle area problem
- Find the maximum volume of a cylinder
Related Questions in ERROR-FUNCTION
- Integral of error-like function
- Approximation of poly of degree 4 by degree 2
- To find the new weights of an error function by minimizing it
- About L2 error distribution and its STRANGE oscillatory behaviour
- Remainder in Asymptotic Expansion of Erfc
- How do I show this :$\int_{-\infty}^{+\infty} x^n 2\cosh( x)e^{-x^2}=0$ if it is true with $n$ odd positive integer?
- Intuitive meaning of attitude error function $\Psi$ defined over $SO(3)$. Is $\Psi$ a metric?
- What are the obtained consequences in mathematics if the antiderivative of $e^{-x²}$ and $e^{x²}$ expressed as elementary functions?
- The maximum area of a circle drawn between the graphs of $e^{-x²}$ and $-e^{-x²}$?
- Evaluation of $\int_{0}^\infty \frac{\sin(x)}{x}e^{- x²} dx$
Related Questions in LINEARIZATION
- Product and Quotient Rule proof using linearisation
- Finding contstant in remainder term for linearization of $exp(x)$
- Linearizing Logarithmic Function
- Stability of Euler's Method for non-linear ODE
- If $ \|G(x+ty)\|<\|G(x)\| $, is then $ \|G(x) + tG'(x)[y]\| <\|G(x)\| $?
- Newtons method for finding reciprocal
- Properties of matrix $T_\epsilon$ such that there exists a unique inverse for $\epsilon \in (-\delta,\delta)$
- (Checking) derivatives of determinant, cofactor, trace
- How to linearize a weighted average with a decision variable?
- LQR Robotic Arm
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
$$|f(x,y)-L(x,y)|=|x^2-3xy-x+6y-2|=$$ $$=|(x-2)^2-3(x-2)(y-1)|\leq$$ $$\leq(x-2)^2+3|(x-2)(y-1)|\leq0.01^2+3\cdot0.1\cdot0.1=0.04.$$ The equality occurs for $x=1.9$ and $y=1.1$, which says that $0.04$ it's the answer.
Done!