# Tagged Questions

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

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### Computer Algebra Systems for Experimental Mathematics (especially Integer Relations with PSLQ)

I would like to use a computer algebra system to do some experimental mathematics, particularly Integer Relation problems using the PSLQ algorithm. I know that Maple has a PSLQ implementation, but I'...
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### Minimizing Area by Approximation

Suppose I have an increasing step function $E_c$ given by $$E_c(\phi) = \sum_{i=1}^n E_i \theta(\phi - \phi_i),$$ where $\theta$ is the Heaviside step function and $E_i$, $\phi$, and $\phi_i$ are all ...
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### Reason for the name “Ring of dual numbers”

The ring of dual numbers over a field $k$ is defined as the quotient $$k[\varepsilon]/\varepsilon^2.$$ I was reading this question with an interesting answer about some of their basic properties and,...
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### Linear approximation to ln(x) at x = 1, then estimate ln(1.08)

I know that the derivative of $\ln(x)$, or log of whatever base (x) = $(1/x)$ *the original function. If x is a more complicated expression, then the derivative would be $(x'/x)*f(x)$. If I knew the ...
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### Linear approximation with two variables

The problem I have is this: Use suitable linear approximation to find the approximate values for given functions at the points indicated: $f(x, y) = xe^{y+x^2}$ at $(2.05, -3.92)$ I know how to do ...
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### % Error of Linear Approximations: Example Problem

I received the following question on my exam and got it right, although it was entirely a guess and I had absolutely no idea how to approach it. Any help with the logic or steps behind this would be ...
I am attempting to find the best path from start to finish from a set of points. Say that one path has costs $x_1,x_2,...,x_n$ and $y_1,y_2,...,y_n$ associated with it. I am attempting to find the ...