Tagged Questions
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1answer
28 views
interpolation question. From MyMaxScore free AP BC Calculus exam.
First, I disagree with the answer sheet. That is why I am posting this question here.
The question: Part B, Question 3a.
The answer given (Sorry for the picture being so small).
I know ...
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1answer
104 views
Derivative of a function defined by the divided difference of another function.
Given a function $f$ of class $C$ $^{n+2}$ in an interval $[a,b]$ and $x_{0}=a<x_1<x_2 ... <x_n = b$ a subdivision of $[a,b]$ into $n+1$ points. Given another function $g$ defined in the ...
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1answer
230 views
A problem on Lagrange interpolation polynomials
Based on a previous question, I had the following conjecture and was wondering if anyone knew how to prove it or find a counterexample.
Consider the polynomial $$ ...
2
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1answer
374 views
Remainder term of Lagrange Interpolation Polynomial
Suppose $x_0,x_1,\ldots,x_n$ are $n+1$ distinct numbers in the interval $[a,b]$ and $f\in C^{n+1}[a,b]$. Then for each $x$ in $[a,b]$, there is a number $\xi$ in $(a,b)$ such that
$$f(x) = P(x) + ...
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1answer
75 views
Interpolation over trajectory at set positions on path
I have the following:
2d vector for velocity
2d start coordinate
gravity acceleration
I need to know the coordinate of a projectile at a given distance along the trajectory.
For example:
...
2
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3answers
189 views
creating smooth curves with f(0) = 0 and f(1) = 1
I would like to create smooth curves, which have f(0) = 0 and f(1) = 1.
What I would like to create are curves similar to the gamma curves known from CRT monitors. I don't know any better way to ...
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3answers
533 views
Smooth transition between two lines (2d)
I have function that is defined as
$$ Y = \frac{1}{15} x \longrightarrow {\rm if}\qquad 0 \leq x \leq 30 $$
$$ Y = \frac{1}{70} x + \frac{11}{7} \longrightarrow {\rm if}\qquad x > 30 $$
The ...
