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

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    Supreme Member Flop21's Avatar
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    Re: MATH1131 help thread

    Why is this true:



    Wouldn't it be 1 real zero?
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    Junior Member parad0xica's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Why is this true:



    Wouldn't it be 1 real zero?
    Why do you think it's 1 real zero?

    I think we need more info

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    Supreme Member Flop21's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by parad0xica View Post
    Why do you think it's 1 real zero?

    I think we need more info
    If it's increasing for one part, then decreasing the other part, then there's 1 point where there's a zero since it's begun to decrease. Where's the other zero?
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    Junior Member parad0xica's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    If it's increasing for one part, then decreasing the other part, then there's 1 point where there's a zero since it's begun to decrease. Where's the other zero?
    What if f: (1,4) -> R such that f(x) = 1000 - (x-3)^2? (no zero)

    We need more info, can you show what example was above this?
    Last edited by parad0xica; 21 Apr 2016 at 6:11 PM.

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    Supreme Member Flop21's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by parad0xica View Post
    What if f: (1,4) -> R such that f(x) = 1000 - (x-3)^2? (no zero)

    We need more info, can you show what example was above this?
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    Junior Member parad0xica's Avatar
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    Re: MATH1131 help thread

    Example says:

    If function is strictly increasing on interval (a,b), then f has exactly one real zero in [a,b]. Note: f(a) and f(b) have opposite signs.

    If function is strictly decreasing on interval (c,d), then f has exactly one real zero in [c,d]. Note: f(c) and f(d) have opposite signs.

    _____

    Our function is strictly increasing on (1,3), so it has exactly one real zero in [1,3]. Note: f(1) and f(3) have opposite signs.

    Our function is strictly decreasing on (3,4), so it has exactly one real zero in [3,4]. Note: f(3) and f(4) have opposite signs.

    Hence, our function has exactly two real zeros in the interval [1,4].
    Last edited by parad0xica; 21 Apr 2016 at 6:23 PM.
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    Junior Member parad0xica's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    If it's increasing for one part, then decreasing the other part, then there's 1 point where there's a zero since it's begun to decrease. Where's the other zero?
    This is not clear...

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    Re: MATH1131 help thread

    Aren't you still in high school ?

    Quote Originally Posted by parad0xica View Post
    Example says:

    If function is strictly increasing on interval (a,b), then f has exactly one real zero in [a,b]. Note: f(a) and f(b) have opposite signs.

    If function is strictly decreasing on interval (c,d), then f has exactly one real zero in [c,d]. Note: f(c) and f(d) have opposite signs.

    _____

    Our function is strictly increasing on (1,3), so it has exactly one real zero in [1,3]. Note: f(1) and f(3) have opposite signs.

    Our function is strictly decreasing on (3,4), so it has exactly one real zero in [3,4]. Note: f(3) and f(4) have opposite signs.

    Hence, our function has exactly two real zeros in the interval [1,4].

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    Junior Member parad0xica's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Zen2613 View Post
    Aren't you still in high school ?
    Why can't I know this if I'm in high school?

    The concepts used in this question can be understood by anyone. It's just that the mathematical language can be frightening and difficult to comprehend but when a diagram pops up, the tunnel will become clear

    Not sure I'm a primary school or high school student or something else.. up to you to deduce and decide :P
    Last edited by parad0xica; 21 Apr 2016 at 6:49 PM.

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    Ancient Orator leehuan's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Zen2613 View Post
    Aren't you still in high school ?
    Huh? I was getting a uni student vibe out of him for a while now.

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    Supreme Member Flop21's Avatar
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    Re: MATH1131 help thread



    Why are the first 2 answers not correct?

    g'(x) = 3x-24x+45, so g(2) = 3 right?

    and

    h'(x) = ln(x-1), so h(2) = 0 ?

    Or am I doing something wrong here?
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    Ancient Orator leehuan's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post


    Why are the first 2 answers not correct?

    g'(x) = 3x-24x+45, so g(2) = 3 right?

    and

    h'(x) = ln(x-1), so h(2) = 0 ?

    Or am I doing something wrong here?
    That derivative g' looks peculiar...

    Let's see the entire question

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    Re: MATH1131 help thread

    Where is the mathsoc solutions to the calculus test 2 past papers??? I can find the solutions for every other test just not calc test 2??

    Pls help.
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    Ancient Orator leehuan's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Where is the mathsoc solutions to the calculus test 2 past papers??? I can find the solutions for every other test just not calc test 2??

    Pls help.
    Yeah me neither. Either the 3rd-5th years are too busy or just forgot about them.

    Not sure who's gonna look after 1131/41 but I'm just gonna upload my 1151 solutions if I get them out...

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    Supreme Member Flop21's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by leehuan View Post
    Yeah me neither. Either the 3rd-5th years are too busy or just forgot about them.

    Not sure who's gonna look after 1131/41 but I'm just gonna upload my 1151 solutions if I get them out...
    FML

    The solutions mathsoc had for the other tests were so good for study haha, they full on explained each answer.
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    Ancient Orator leehuan's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    FML

    The solutions mathsoc had for the other tests were so good for study haha, they full on explained each answer.
    Ikr. But don't complain lol they didn't even have to do them

    Just like InteGrand doesn't exactly have to help me but I'll always be grateful of it
    Last edited by leehuan; 28 Apr 2016 at 1:09 PM.

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    Supreme Member Flop21's Avatar
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    Re: MATH1131 help thread

    Just confirming I'm correctly using the definition of the derivative:

    So to show that f(x) = x^2 then f'(x) = 2x, you get the formula, sub in and after expanding and simplifying you get 2x+h. Now as h -> 0, h = 0, so we make h = 0 and then we are left with 2x.

    Is this how you use it? I.e. finding the limit as h -> 0, which is 0...? or???
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    Ancient Orator leehuan's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Just confirming I'm correctly using the definition of the derivative:

    So to show that f(x) = x^2 then f'(x) = 2x, you get the formula, sub in and after expanding and simplifying you get 2x+h. Now as h -> 0, h = 0, so we make h = 0 and then we are left with 2x.

    Is this how you use it? I.e. finding the limit as h -> 0, which is 0...? or???
    Correct. Basically if you had to blindly show that you substitute the formula into the definition of the derivative, and from memory 2x+h is a correct step.


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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Just confirming I'm correctly using the definition of the derivative:

    So to show that f(x) = x^2 then f'(x) = 2x, you get the formula, sub in and after expanding and simplifying you get 2x+h. Now as h -> 0, h = 0, so we make h = 0 and then we are left with 2x.

    Is this how you use it? I.e. finding the limit as h -> 0, which is 0...? or???
    Yeah, that's how you get 2x. (This is something done in 2U I'm pretty sure.)

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    Supreme Member Flop21's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by InteGrand View Post
    Yeah, that's how you get 2x. (This is something done in 2U I'm pretty sure.)
    Really? I feel like it's kind of familiar... but don't remember ever actually being asked to use it.
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Really? I feel like it's kind of familiar... but don't remember ever actually being asked to use it.
    Finding derivatives from first principles is in the 2U syllabus, surely? And if it is, finding the derivative of x^2 would be a typical example.

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    Supreme Member Flop21's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by InteGrand View Post
    Finding derivatives from first principles is in the 2U syllabus, surely? And if it is, finding the derivative of x^2 would be a typical example.
    Hehe you're right. Just saw some examples in last year's 2u marathon.

    You can tell there were certain things in 2u I just didn't pay attention to.
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    Ancient Orator leehuan's Avatar
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    Re: MATH1131 help thread

    Quote Originally Posted by Flop21 View Post
    Hehe you're right. Just saw some examples in last year's 2u marathon.

    You can tell there were certain things in 2u I just didn't pay attention to.
    Tbh, almost all of my cohort just ignored it and counted on the fact it wouldn't be examined in the paper.

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    Supreme Member Flop21's Avatar
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    Re: MATH1131 help thread

    f(x) = x|x|

    If it exists, evaluate lim h->0+ [f(0+h) - f(0)] / h


    What do I even do here? Why have they got 0 already in the formula?
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    Ancient Orator leehuan's Avatar
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    Re: MATH1131 help thread

    They want you to find lim h->0 f'(0)

    Note that x=0 does not strictly imply the same thing as h=0
    Also note that f(0) = 0

    So if you want to find lim h->0+ f(h)/h

    Note that as h approaches 0 from the right, x = x and |x| = x
    (Instead if h approaches from the 0 left, x = x but |x| = -x)

    So they want you to see if there's an answer to lim h->0+ h|h|/h

    (Apologies for poor wording)
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