UNSW 1st year finals Q (1 Viewer)

integral95

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Hey Ya I just had my final maths exam today, and some questions rekt me hard lol, and ODE (ordinary differential equation) question and a weird limit one






need a pro guy to help here hehe
 
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seventhroot

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can't do the first one; probably some syntax error

Q2) ln(c)

2ez

NOTE: utilized the "otherwise"
 

anomalousdecay

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I got zero for the second one in the test, then my mate convinced me its just c by using calculator trial and error, now I'm convinced its ln (c) :haha:
 

anomalousdecay

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I found the first derivative as:



So we get that result from y(0) = 0.

I found the implicit derivative with respect to x as:



Then I got that when we substitute y(0) = 0, we get the second derivative is equal to zero.

Now derive once more....





Yeah I stuffed up in the exam.... The answer actually is:



I did too many sillies that exam.... Gonna cost me HD. Just really wasn't my day... That exam made me feel so sad because I knew everything (except one probability question) but in the exam couldn't do it and write everything down properly. Missed the hyperbolic sine integral for q4 completely too....
 

integral95

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NOOOOOO WHY DID NOT THINK OF L'HOPITAL!!!!! I WILL NEVER FORGET THIS NEXT TIME
Ahh well thanks anyways
 
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anomalousdecay

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Still not sure if I did the other one correctly lol....

Does it look valid?
 

seanieg89

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I found the first derivative as:



So we get that result from y(0) = 0.

I found the implicit derivative with respect to x as:



Then I got that when we substitute y(0) = 0, we get the second derivative is equal to zero.

Now derive once more....





Yeah I stuffed up in the exam.... The answer actually is:



I did too many sillies that exam.... Gonna cost me HD. Just really wasn't my day... That exam made me feel so sad because I knew everything (except one probability question) but in the exam couldn't do it and write everything down properly. Missed the hyperbolic sine integral for q4 completely too....
Are you sure about that answer? I think (*) is incorrect, as well as the Maclaurin series.

I think it should be

y(x)=x-x^3/2 to 3rd order (and y'''(0)=-3).
 

anomalousdecay

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Are you sure about that answer? I think (*) is incorrect, as well as the Maclaurin series.

I think it should be

y(x)=x-x^3/2 to 3rd order (and y'''(0)=-3).
Yep that's a mistake thanks for spotting that. Your final solution fixes up my error.

Ironically, I got closer to that in the exam (just had x^2 instead of x^3 as I have written down on my question paper when I wanted to check later on). I was more worried that my method seemed wrong completely.

We actually had no practice on such a question in our homework questions I believe (integral, seventh, confirm if this is true or not), so I just wanted to know that I had made the most of my understanding of ODE's from the course.

Thanks for the help again :D

Need to spread more rep.
 

seventhroot

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Yep that's a mistake thanks for spotting that. Your final solution fixes up my error.

Ironically, I got closer to that in the exam (just had x^2 instead of x^3 as I have written down on my question paper when I wanted to check later on). I was more worried that my method seemed wrong completely.

We actually had no practice on such a question in our homework questions I believe (integral, seventh, confirm if this is true or not), so I just wanted to know that I had made the most of my understanding of ODE's from the course.

Thanks for the help again :D

Need to spread more rep.
done for you :D
 

FrankXie

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Hey Ya I just had my final maths exam today, and some questions rekt me hard lol, and ODE (ordinary differential equation) question and a weird limit one






need a pro guy to help here hehe
are you sure the first question is really like that? I guess you missed a y on RHS? like

the second question can be solved, other than L'Hospital rule, using equivalent substitution like

 

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