• Cyberian's Gold

    Given the following data x:4 5 7 10 y:46 102 294 346 Value of 1st order divided difference f[5 , 7] is

    91
    92
    94
    96

  • Cyberian's Gold

    Forthegivendatapoints(x0,y0),(x1y1),(x2y2),and(x3,y3)thezero−orderdividedifferencewillbegivenas

    cf4ff410-1c08-454c-b055-a75a87c6c597-image.png
    5a3820f4-2c5d-4a9a-adb1-445e60017b0e-image.png

  • Cyberian's Gold

    Forthegivendatapoints(4,45),(5,104),and(6,190),thezero−orderdividedifferencewillbe

    3ecd2368-2b48-4e0a-83ae-0e937ffa8f88-image.png

  • Cyberian's Gold

    For the following data

    5c89a396-1322-4a06-9459-bb6a0534787f-image.png

    70887022-15d6-4d8e-a20f-a02195ed59a4-image.png

  • Cyberian's Gold

    Whichofthefollowingmethodcanbeusedforinterpolationforthegivenvaluesofxandy?x y0.30.0670.70.2480.90.518

    Lagrangens interpolation

  • Cyberian's Gold

    If y(x) is approximated by a polynomial Pn(x) of degree n then the error is given by

    ε(x)=y(x)+Pn(x)
    ε(x)=y(x)−Pn(x)
    ε(x)=y(x)×Pn(x)
    ε(x)=y(x)÷Pn(x)

  • Cyberian's Gold

    @zaasmi said in MTH603 Quiz 2 Solution and Discussion:

    Forthegivendividedifferencetablex 1 4 7y2.23.54.11stD.D0.43330.22ndD.D−0.0389theNewton′sdividedifferenceinterpolationformulawillbe

    y=f(x)=2.2+(x−1)(−0.0389)+(x−1)((x−4)(0.4333)

    y=f(x)=2.2+(x−1)(0.4333)+(x−1)((x−4)(−0.0389)

    y=f(x)=−0.0389+(x−1)(0.4333)+(x−1)((x−4)(2.2)

    y=f(x)=−0.0389+(x−1)(2.2)+(x−1)((x−4)(0.4333)

    1d767974-39ce-409c-818f-505d317238cc-image.png

    Solution:

    c58d97cf-c1fa-46aa-add5-3cb89de6f935-image.png 74e3b9b6-be5c-46dc-8ecc-0c4f775cfe60-image.png

  • Cyberian's Gold

    Forthegivendividedifferencetablex 1 4 7y2.23.54.11stD.D0.43330.22ndD.D−0.0389theNewton′sdividedifferenceinterpolationformulawillbe

    y=f(x)=2.2+(x−1)(−0.0389)+(x−1)((x−4)(0.4333)

    y=f(x)=2.2+(x−1)(0.4333)+(x−1)((x−4)(−0.0389)

    y=f(x)=−0.0389+(x−1)(0.4333)+(x−1)((x−4)(2.2)

    y=f(x)=−0.0389+(x−1)(2.2)+(x−1)((x−4)(0.4333)

    1d767974-39ce-409c-818f-505d317238cc-image.png

  • Cyberian's Gold

    Whatwillbethevalueof′a′inthegivendividedifferencetable? x2468y0.51.11.72…21stD.D0.30.30.252ndD.Da−0.01253rdD.D−0.0021

    e0d49474-f272-41dc-bb69-4fd9f6e1af61-image.png

  • Cyberian's Gold

    @zaasmi said in MTH603 Quiz 2 Solution and Discussion:

    For the given data points (1,0.3),(3,1),and(5,1.2) the divide difference table will be given as

    219e6e10-947a-4ef6-8072-8df332b2257e-image.png

    0e268c65-269c-4352-b66a-ee4fd412055e-image.png

    Forthegivendatapoints(1,0.3),(3,1),and(5,1.2)thedividedifferencetablewillbegivenas

  • Cyberian's Gold

    For the given data points (1,0.3),(3,1),and(5,1.2) the divide difference table will be given as

    219e6e10-947a-4ef6-8072-8df332b2257e-image.png

    0e268c65-269c-4352-b66a-ee4fd412055e-image.png

  • Cyberian's Gold

    @zaasmi said in MTH603 Quiz 2 Solution and Discussion:

    Δ=----- ?

    E−1/2
    1-E
    E-1
    None

    b050ee38-f1b6-4728-919c-2ea1eb3b4dd4-image.png

  • Cyberian's Gold

    Δ=----- ?

  • Cyberian's Gold

    In Lagrange’s interpolation, for the given five points we can represent the function f (x) by a polynomial of degree

    3
    4
    5
    6

  • Cyberian's Gold

    In Simpson’s 1/3 rule, the global error is of ………………

    O(h2)
    O(h3)
    O(h4)
    None of the given choices

  • Cyberian's Gold

    Integration is a ………………process.

    Subtracting
    Summing
    Dividing
    None of the given choices

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