Halp with math1001 sample quiz!!! (1 Viewer)

[LookingAtYOU]

Hey guys could you please help me get full working out + answers for these questions?
+rep to anyone who HALPED
Link to Questions: http://www.maths.usyd.edu.au/u/UG/JM/MATH1001/r/2012-quiz-sample.pdf

Thanks in advance!

 

[OzKo]

Which questions were you having trouble with exactly?

Also, it is best for you to tell us why you're confused so we can help fix that too. If we just blindly throw answers at you, you won't learn much at all.

If you actually read the instructions, there is a list of tutorial questions related to the quiz. If you know how to do the questions, then the quiz should be simpler.

You're not going to learn much if we just give you the solutions, so you're better off attempting it, looking at which ones you get wrong, and then asking us for help from there.

Please rephrase your request.

 

[LookingAtYOU]

Pls, can somebody show me how to do Q4 and Q14? (Show me steps/working out)
My test is next week and im stumped on these questions...

Many thanks!

 

[zxreth]

Pls, can somebody show me how to do Q4 and Q14? (Show me steps/working out)
My test is next week and im stumped on these questions...

Many thanks!

Question 4: convert to polar form so you get sqrt(2)cis(pi/4) then use de moivres theorem, so that you get (sqrt(2))^6 cis(6pi/4), then simplify for answer.

With question 14, i'd appreciate some help too.

 

[Riproot]

Isn't a critical point just like finding a horizontal point of inflexion?

I'll totes get onto it when I get home.

 

[funnytomato]

Pls, can somebody show me how to do Q4 and Q14? (Show me steps/working out)
My test is next week and im stumped on these questions...

Many thanks!

Q14

the way to find critical point for this question is similar to that for function of 1 variable( i.e. where f'(x)=0 ),
since the function has more than just one variable, you'll need to find its Partial Derivatives
find the x and y partial derivatives by regarding y and x as constants , respectively

the critical point is where both x and y partials are 0
so you'd need to solve:
df/dx=...=0
and df/dy=...=0
simultaneously
(the 'd' is meant to be the 'backwards 6 d')

and then you can get the coordinates of the critical point

 

[Carrotsticks]

Isn't a critical point just like finding a horizontal point of inflexion?

I'll totes get onto it when I get home.

Not necessarily. We have other types of critical points too.

 

[zxreth]

Not necessarily. We have other types of critical points too.

Thanks for that

 

[nml10]

For question 10, do you just substitute (0,0) to the equation z = e^(x+y) - 2 ? If not, how do you approach the question?

 

[Riproot]

Not necessarily. We have other types of critical points too.

Yeah, I deffs could've phrased that better.

 

[funnytomato]

For question 10, do you just substitute (0,0) to the equation z = e^(x+y) - 2 ? If not, how do you approach the question?

yes

z = e^(0+0) - 2 = -1 is the minimum for the given domain

 

[LookingAtYOU]

Hey Carrotsticks, you seem like a really good maths person!
Could you help me out with Q's 2,4,6,8 ?
I'm really struggling with this unit because I only took up 2Unit maths in highschool.

 

[LookingAtYOU]

Pls reply ASAP as I have my quiz coming up on Tuesday!!!

Thank you

 

[Riproot]

Just solve Q2 and it's I'm pretty sure.

Oh wait, you have answers.

Pretty much just find cos(pi/6) and sin(pi/6)

Then times by (2 + i)

So



and solve from there(?)

(That doesn't look right. I need to do this on paper.)

 

[LookingAtYOU]

Riproot, your taking the ADV math units right?

 

[Riproot]

WAIT!

Modulus.

Find the modulus.

Far out. How did I not see that?!

 

[Riproot]

Riproot, your taking the ADV math units right?

Yep, but I think I'm in the bottom half of the pack. lol (I get the first quiz marks for MATH1901 on Monday)

Okay. I got it.

Just take the modulus of (2 + i) and (cos(pi/6) - isin(pi/6)) and times them together.

(2 + i) = Rcis(theta)




Then the modulus of the other one is 1 because it is already in cos(theta) + isin(theta) form and R = 1.

Therefore,

 

[LookingAtYOU]

Wait, how do you find the modulus of (cos(pi/6) - isin(pi/6))?

 

[Riproot]

Q4

LET

 

[LookingAtYOU]

Thanks for the quick response bro! appreciate it heaps.