PPT4

PPT4

University

10 Qs

quiz-placeholder

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PPT4

PPT4

Assessment

Quiz

Mathematics

University

Practice Problem

Hard

Created by

yanna may

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10 questions

Show all answers

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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