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Thread: First Year Mathematics A (Differentiation & Linear Algebra)

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    Re: MATH1131 help thread

    Can someone do this via l'hopital's rule? Answer is 3, which I'm not getting for some odd reason.

    lim x -> 1 (2x^4-3x^3+x)/((x-1)^2)
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Can someone do this via l'hopital's rule? Answer is 3, which I'm not getting for some odd reason.

    lim x -> 1 (2x^4-3x^3+x)/((x-1)^2)
    Did you keep re applying the rule
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    Re: MATH1131 help thread

    Can someone also do this question, I'm not getting the right answer.

    Differentiate x + ln(x) = y + 2ln(y)


    I keep getting 1 + 1/x - 2/y
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    Junior Member parad0xica's Avatar
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    Re: MATH1131 help thread

    Clue 1: 121 112
    Who am I?

    ( ͡° ͜ʖ ͡°) ( ͡° ͜ʖ ͡°)Clue 2

    Clue 0: Clockwise

    Clue 3: Are you watching closely? ∃ a clue every now and then
    Clue 4: 99 115
    Clue 5: |℘(S)| = 15^2 + 31

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    Re: MATH1131 help thread

    Quote Originally Posted by turntaker View Post
    Did you keep re applying the rule
    Yeah and I got 6 not 3
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    Re: MATH1131 help thread

    Quote Originally Posted by parad0xica View Post
    Oh right thanks, yeah my mistake was silly, missing out 2 on the bottom.
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    Junior Member parad0xica's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Can someone also do this question, I'm not getting the right answer.

    Differentiate x + ln(x) = y + 2ln(y)


    I keep getting 1 + 1/x - 2/y
    With respect x?
    Clue 1: 121 112
    Who am I?

    ( ͡° ͜ʖ ͡°) ( ͡° ͜ʖ ͡°)Clue 2

    Clue 0: Clockwise

    Clue 3: Are you watching closely? ∃ a clue every now and then
    Clue 4: 99 115
    Clue 5: |℘(S)| = 15^2 + 31

  8. #108
    Metallic Oxide iforgotmyname's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Can someone also do this question, I'm not getting the right answer.

    Differentiate x + ln(x) = y + 2ln(y)


    I keep getting 1 + 1/x - 2/y
    You forgot about the chain rule at the end. And f'x of y is dy/dx
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    Re: MATH1131 help thread

    Quote Originally Posted by parad0xica View Post
    With respect x?
    Uhhhh not sure. It's implicit differentiation sorry. It's part of a equation of a line tangent question.
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    Junior Member parad0xica's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Uhhhh not sure. It's implicit differentiation sorry. It's part of a equation of a line tangent question.
    To demonstrate iforgotmyname's comment:



    Differentiate all terms with respect to x,





    Last edited by parad0xica; 1 May 2016 at 11:12 PM.
    Flop21 likes this.
    Clue 1: 121 112
    Who am I?

    ( ͡° ͜ʖ ͡°) ( ͡° ͜ʖ ͡°)Clue 2

    Clue 0: Clockwise

    Clue 3: Are you watching closely? ∃ a clue every now and then
    Clue 4: 99 115
    Clue 5: |℘(S)| = 15^2 + 31

  11. #111
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    Re: MATH1131 help thread

    Why can't I used chain rule to differentiate sqrt(x-1), e.g. (x-1)^1/2... y'= 1/2(x-1)*1

    Instead the answers use the definition of a derivative to solve and get a different answer. Am I doing something wrong above^?
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Why can't I used chain rule to differentiate sqrt(x-1), e.g. (x-1)^1/2... y'= 1/2(x-1)*1

    Instead the answers use the definition of a derivative to solve and get a different answer. Am I doing something wrong above^?

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    Re: MATH1131 help thread

    Quote Originally Posted by InteGrand View Post
    So you get different derivatives using normal methods vs the definition?

    The question is a Mean Value Theorem question, with that function on an interval.
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    So you get different derivatives using normal methods vs the definition?

    The question is a Mean Value Theorem question, with that function on an interval.
    We should get the same answer.

    I can't see the specific Q., but if it's that function over an interval (assuming it's well-defined there, i.e. x > 1 there), then the derivative should be what I posted.

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    Re: MATH1131 help thread

    Quote Originally Posted by InteGrand View Post
    We should get the same answer.

    I can't see the specific Q., but if it's that function over an interval (assuming it's well-defined there, i.e. x > 1 there), then the derivative should be what I posted.
    It is, but what I'm I doing incorrect? Or how are you getting that derivative?
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    It is, but what I'm I doing incorrect? Or how are you getting that derivative?


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    Re: MATH1131 help thread

    Quote Originally Posted by InteGrand View Post
    Oh my. I was forgetting to do the 0.5-1 to the power.

    Thanks appreciate it InteGrand.
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    Re: MATH1131 help thread



    How do I solve this with MAPLE?
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    Re: MATH1131 help thread

    How do I do this in MAPLE?



    I understand you use sum(); but what do you do with the n^5/2 on the left??
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    Re: MATH1131 help thread

    How do I solve this in MAPLE?



    My incorrect attempt was to go... s:= [solve(expression)] then allvalues(s[1]); to find first root... same for all other roots, then evalf(result, 10); on each root.

    Anyone know the steps to the correct way to get right answers?
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    How do I do this in MAPLE?



    I understand you use sum(); but what do you do with the n^5/2 on the left??
    The expression in the limit is not a sum, but rather a product. This is because that symbol is capital Pi (), which is used for products. The symbol for summation is a capital Sigma ().

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    Re: MATH1131 help thread

    Quote Originally Posted by InteGrand View Post
    The expression in the limit is not a sum, but rather a product. This is because that symbol is capital Pi (), which is used for products. The symbol for summation is a capital Sigma ().
    yeah sorry I actually meant product(); originally.
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    Re: MATH1131 help thread

    bump someone help me with these MAPLE questions pls
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    How do I do this in MAPLE?



    I understand you use sum(); but what do you do with the n^5/2 on the left??
    Try

    limit(n^(5/2)*(product(2*k/(2*k+5), k = 1 .. n)), n = infinity)
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    How do I solve this in MAPLE?



    My incorrect attempt was to go... s:= [solve(expression)] then allvalues(s[1]); to find first root... same for all other roots, then evalf(result, 10); on each root.

    Anyone know the steps to the correct way to get right answers?
    Close, but maple can calculate all roots for a polynomial like that at once, so you don't need to specify an interval. Your first part, solve z for p(z)=0 is correct. This doesn't give numerical values though, so you need to use evalf.

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