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First Year Mathematics A (Differentiation & Linear Algebra) (2 Viewers)

InteGrand

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Re: MATH1131 help thread

Think I'm just confused how to do these questions involving fractions you cannot simplify and have to do with integration by parts. Can do integration by parts if it's just f(x)*g(x).
 

Red_of_Head

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Re: MATH1131 help thread

How do we do that?

Think I'm just confused how to do these questions involving fractions you cannot simplify and have to do with integration by parts. Can do integration by parts if it's just f(x)*g(x).
So the numerator becomes f(x) and 1/denominator becomes g(x).

To integrate 1/(1+x)^3, change it to (1+x)^-3, and then the normal integration process, changing back to the fraction for the final result.
 

Flop21

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Re: MATH1131 help thread

Find the arg(z) of z= -1-i

I'm getting the wrong answer.
 

InteGrand

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Re: MATH1131 help thread

Yeah I did get pi/4.
I'm guessing you did inverse tan of (-1/-1).

Since the real part of the complex number is negative, we need to add or subtract pi from what you got by doing that. Since the imaginary part is negative, we subtract pi. So the answer is pi/4 – pi = -3pi/4.

It's easier to do this one graphically though. The relevant point is (-1,-1), which is in quadrant 3 and lies on the 45 degree line y = x, so the angle it makes to the positive x-axis is -3pi/4.
 

Flop21

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Re: MATH1131 help thread

I'm guessing you did inverse tan of (-1/-1).

Since the real part of the complex number is negative, we need to add or subtract pi from what you got by doing that. Since the imaginary part is negative, we subtract pi. So the answer is pi/4 – pi = -3pi/4.

It's easier to do this one graphically though. The relevant point is (-1,-1), which is in quadrant 3 and lies on the 45 degree line y = x, so the angle it makes to the positive x-axis is -3pi/4.

Ohhh okay we subtract pi. I was originally trying to add pi. Thanks
 

Flop21

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Re: MATH1131 help thread

How do I sketch this region???

{z (element symbol) C : 0<=Arg(z-i) <= pi/4}


I'm confused with the arg part.
 

leehuan

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Re: MATH1131 help thread

How do I sketch this region???

{z (element symbol) C : 0<=Arg(z-i) <= pi/4}


I'm confused with the arg part.
Because we're talking about z-i, we need to consider the point (0,1)



So for the part: arg(z-i) = 0

We draw a ray at an angle of 0 (so, just pointing to the right) from the point (0,1).

For the other part: arg(z-i) = pi/4
We draw a ray at an angle of pi/4 from the point (0,1) instead

And we put in a discontinuity at the point (0,1) because we don't include it (this is just a hole in the graph)

If you're interested, a geometric interpretation would be the lines y=1 and y=x+1, but just the top halves of the line

Because we have 0<=arg(z-i)<=pi/4, we shade all the region that's between these two lines.

The geometric interpretation would then be x>0, y>=1, y<=x+1
 

Flop21

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Re: MATH1131 help thread

I'm having a lot of trouble with these questions, any tips or places I can go to see these done more?


Or here's another one of these questions if someone wants to show me the working that'd be awesome:

They give you A, A^2, A^4, A^8, and ask for the inverse of A^7.

A^8 is 16I also.
 

InteGrand

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Re: MATH1131 help thread

I'm having a lot of trouble with these questions, any tips or places I can go to see these done more?


Or here's another one of these questions if someone wants to show me the working that'd be awesome:

They give you A, A^2, A^4, A^8, and ask for the inverse of A^7.

A^8 is 16I also.
 

Flop21

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Re: MATH1131 help thread



Why is this true? What happens with the "z -("part?
 

Flop21

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Re: MATH1131 help thread

Oh lord, I've got 1 whole day left to study for this exam.

I just want to pass but not sure if possible.
 

iforgotmyname

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Re: MATH1131 help thread

Oh lord, I've got 1 whole day left to study for this exam.

I just want to pass but not sure if possible.
You can get lower than 50 in the finals and still pass. Just putting it out there
 

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