Questions tagged [linear-approximation]

For questions about linear approximations, $f(x) \approx f(a)+f'(a)(x-a)$ for $x$ around $a$.

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Can someone help me attempt this question? I don't know what equations to propose. Thank You.. [closed]

Propose a nonlinear system of equations that contains at least four variables, and its corresponding initial approximation to solve the equations. The initial approximation should contain both ...
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What is the purpose of taking the linear approximation of this tangent function for estimating the measurement error?

$h$ = distance from ground to eye of a person, who measured the angle to the top of the building with a protractor. $θ$ = from the eye to the top of the building. $x$ = distance of the person from the ...
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Best linear approximation for x(x-y)

I have a non-linear term in the form of $$x(x-y)$$ I need to replace it with a linear term in the form of $$c_1x-c_2y$$ I have seen the following linear approximation in literature but I need to know ...
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Response surface and variables importance

Disclaimer: I'm not expert in math; the solution to this problem may be trivial. I have a process based on a deterministic computer simulation where two continuous input variables $x_1$ and $x_2$ (...
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How can I use for the generalized logistic equation a series approximation?

The question is how can I show the following approximation stated in this paper. I have tried to follow , but I am not pretty sure if the following results are correct Generalized logistic growth ...
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Two dimensional Taylor Series Linear Approximation

Hi so I'm Currently studying Multivariable Calculus and Real Analysis and have came to a wall on this question. I know from reading my notes that I have to find F(x,y), Fx(x,y), Fy(x,y), Fxx(x,y), Fyy(...
A linear approximation of a function $f:\mathbb{R} \to \mathbb{R}$ at the point $x=a$ draws a tangent line to $f(x)$ at $(a,f(a))$ and approximates values of $f(x)$ for $x$ near $a$ by using the ...