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  • Andreas's copy of MA100 MT Week 9

    by Andreas Vohns and 1 other

    This is the question for week 9 of the MA100 course at the LSE. It looks at material from chapters 17 and 18.

    Description of variables for part b:
    For part b we want to have four functions such that the derivative of one of them, evaluated at 0, gives 0; but for the rest we do not get 0. We also want two of the ones that do not give 0, to be such that the derivative of their sum, evaluated at 0, gives 0; but when we do this for any other sum of two of our functions, we do not get 0. Ultimately this part of the question will show that even if two functions are not in a vector space (the space of functions with derivate equal to 0 when evaluated at 0), then their sum could nonetheless be in that vector space. We want variables which statisfy:

    a,b,c,d,f,g,h,j,k,l,m,n are variables satisfying

    Function 1: x^2 + ax + b sin(cx)
    Function 2: x^2 + dx + f sin(gx)
    Function 3: x^2 + hx + j sin(kx)
    Function 4: x^2 + lx + m sin(nx)

    u,v,w,r are variables satifying
    u=a+bc
    v=d+fg
    w=h+jk
    r=l+mn

    The derivatives of each function, evaluated at zero, are:
    Function 1: u
    Function 2: v
    Function 3: w
    Function 4: r

    So we will define
    u as random(-5..5 except(0))
    v as -u
    w as 0
    r as random(-5..5 except(0) except(u) except(-u))

    Then the derivative of function 3, evaluated at 0, gives 0. The other functions give non-zero.
    Also, the derivative of function 1 + function 2 gives 0. The other combinations of two functions give nonzero.

    We now take b,c,f,g,j,k,m,n to be defined as \random(-3..3 except(0)).
    We then define a,d,h,l to satisfy
    u=a+bc
    v=d+fg
    w=h+jk
    r=l+mn

    Description for variables of part e:

    Please look at the description of each variable for part e in the variables section, first.
    As described, the vectors V3_1 , V3_2 , V3_3 are linearly independent. We will simply write v1 , v2 , v3 here.
    In part e we ask the student to determine which of the following sets span, are linearly independent, are both, are neither:

    both: v1,v2,v3
    span: v1,v1+v2,v1+v2+v3, v1+v2+v3,2*v1+v2+v3
    lin ind: v1+v2+v3
    neither: v2+v3 , 2*v2 + 2*v3
    neither:v1+v3,v1-2*v3,2*v1-v3
    neither: v1+v2,v1-v2,v1-2*v2,2*v1-v2

    Question Draft

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    Last modified 11/09/2019 07:45

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  • Vector addition by summing scalar components

    Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

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    Last modified 10/09/2019 14:47

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    Stage 2

  • Vector addition by summing scalar components

    by Chris King and 1 other

    Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

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    Last modified 12/07/2019 05:09

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  • Geometric $\sum$ questions 2

    by Xiaodan Leng and 1 other

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    Last modified 11/07/2019 06:52

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  • Geometric $\sum$ questions 2

    by Xiaodan Leng and 1 other

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    Last modified 11/07/2019 06:51

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  • Understanding $\sum$ notation - fixed sum

    by Xiaodan Leng and 1 other

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    Last modified 11/07/2019 06:29

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  • Understanding $\sum$ notation

    by Xiaodan Leng and 1 other

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    Last modified 11/07/2019 06:29

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  • Linear regression (employe test scores)

    by Xiaodan Leng and 1 other

    Find a regression equation.

    Now includes a graph of the regression line and another interactive graph gives users the opportunity to move the regression line around. Could be used for allowing users to experiment with what they think the line should be and see how this compares with the calculated line.

    Also includes an updated SSE to see how the sum of the squares of the residuals varies with the regression line.

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    Last modified 11/07/2019 05:21

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  • Partial sum of an arithmetic sequence - birthday money

    by Xiaodan Leng and 2 others

    The amount of money a person gets on their birthday follows an arithmetic sequence.

    Calculate the amount on a given birthday, then calculate the sum up to that point.

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    Last modified 11/07/2019 01:54

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  • Compute the partial sum of an arithmetic sequence

    by Xiaodan Leng and 2 others

    Given the first and last terms of a finite arithmetic sequence, calculate the number of elements and then the sum of the sequence.

    Each part is broken into steps, with the formula given.

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    Last modified 11/07/2019 01:51

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