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

1. ## 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)  Reply With Quote

2. ## Re: MATH1131 help thread Originally Posted by Flop21 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  Reply With Quote

3. ## 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  Reply With Quote

4. ## Re: MATH1131 help thread  Reply With Quote

5. ## Re: MATH1131 help thread Originally Posted by turntaker Did you keep re applying the rule
Yeah and I got 6 not 3  Reply With Quote

6. ## Re: MATH1131 help thread Originally Posted by parad0xica Oh right thanks, yeah my mistake was silly, missing out 2 on the bottom.  Reply With Quote

7. ## Re: MATH1131 help thread Originally Posted by Flop21 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?  Reply With Quote

8. ## Re: MATH1131 help thread Originally Posted by Flop21 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  Reply With Quote

9. ## Re: MATH1131 help thread Originally Posted by parad0xica With respect x?
Uhhhh not sure. It's implicit differentiation sorry. It's part of a equation of a line tangent question.  Reply With Quote

10. ## Re: MATH1131 help thread Originally Posted by Flop21 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,  Reply With Quote

11. ## 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^?  Reply With Quote

12. ## Re: MATH1131 help thread Originally Posted by Flop21 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^?  Reply With Quote

13. ## Re: MATH1131 help thread Originally Posted by InteGrand 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.  Reply With Quote

14. ## Re: MATH1131 help thread Originally Posted by Flop21 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.  Reply With Quote

15. ## Re: MATH1131 help thread Originally Posted by InteGrand 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?  Reply With Quote

16. ## Re: MATH1131 help thread Originally Posted by Flop21 It is, but what I'm I doing incorrect? Or how are you getting that derivative?  Reply With Quote

17. ## Re: MATH1131 help thread Originally Posted by InteGrand Oh my. I was forgetting to do the 0.5-1 to the power.

Thanks appreciate it InteGrand.  Reply With Quote

18. ## Re: MATH1131 help thread How do I solve this with MAPLE?  Reply With Quote

19. ## 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??  Reply With Quote

20. ## Re: MATH1131 help thread

How do I solve this in MAPLE? My incorrect attempt was to go... s:= [solve(expression)] then allvalues(s); 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?  Reply With Quote

21. ## Re: MATH1131 help thread Originally Posted by Flop21 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 ().  Reply With Quote

22. ## Re: MATH1131 help thread Originally Posted by InteGrand 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.  Reply With Quote

23. ## Re: MATH1131 help thread

bump someone help me with these MAPLE questions pls  Reply With Quote

24. ## Re: MATH1131 help thread Originally Posted by Flop21 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)  Reply With Quote

25. ## Re: MATH1131 help thread Originally Posted by Flop21 How do I solve this in MAPLE? My incorrect attempt was to go... s:= [solve(expression)] then allvalues(s); 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.  Reply With Quote

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