
PPT4
Quiz
•
Mathematics
•
University
•
Practice Problem
•
Hard
yanna may
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the supremum norm denoted as in the given text?
∥f∥a,b,∞
∥f∥
∥f∥∞
∥f∥a,b
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the characteristic Lagrange polynomial for the given function f?
Lagrange Interpolation
Piecewise Lagrange Interpolation
Newton-Cotes Formulas
Gaussian Quadrature
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the error bound for the Lagrange interpolating polynomial?
max(x∈[a,b])|f(x)|
∥f∥a,b,∞
∥f∥∞
(b−a)n+1/(n+1)!
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the degree of precision for the interpolatory quadrature QI_n?
∥f∥a,b,∞
max(x∈[a,b])|f(x)|
max{m∈N:E_n[p]=0 for all p∈Pm}
∥f∥∞
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the approximate value of the integral Zxkxk−1f(x)dx using the given quadratic polynomial P2(x)?
h(f(q)+f(s))
h/4(f(q)+2f(r)+f(s))
h/2(f(q)+f(r))
h/3(f(q)+4f(r)+f(s))
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the maximal degree of precision for numerical quadratures having n+1 nodes?
n^2
2n+1
2n
n
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the largest possible degree of precision for a numerical quadrature Qn?
n
2n
2n+1
n^2
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