Math Is Fun Forum

Hi,

I am doing first year uni maths and i was wondering if someone could please help with the following question?

By multiplying together known Maclaurin Series obtain the expansion of (cos2x)log(1+x²) up to term x^6.

I have found co2x to be 1- 2x² + 2/3x^4 - 4/45x^6 + ...

and log(1+x²) to be tan-¹x = x - 1/3x³ + 1/5x^5 +...

By multiplying these values together I am not getting the correct answer and I don't have a clue where I'm going wrong.  The solution I have is x² - 5/2x^4 + 2x^6.

I would be grateful for any help or corrections if I am doing this completely wrong.

Thank you.

Hi,

I am doing 1st year university algebra.  I was wondering if anyone could tell me if i have done this question correctly?

Q.  Let u and v be perpendicular vectors of lengths 1 and 2 respectively.  Evaluate (3u+v) • (u-2v).

By expanding the bracket I get

3(u.u)-5(u.v)-2(v.v)

Since u is a unit vector u.u=1 and as they are perpendicular u.v=0

Hence 3(1) - 5(0) - 8 = -5.

Is this correct i am unsure of what to do with v.v as v is of length 2 therefore not a unit vector so I just took the square of 2.

I would be grateful for any help with this.

Thanks

Hi i was wondering if anyone could help me with the following question

∫sin(√ x)/√ x

I have a few ways which i could do this i'm just not sure what is the correct answer.

Thank you

Natkirky

Hi,

I was wondering if someone could help with this question:

Show:  1 - cosθ/sinθ = sinθ/1 + cosθ

I can get all other variations of this to work and i can only get this to work the wrong way around ie 1 + cosθ/sinθ, so I know it's something really stupid I am missing.

I would be grateful for any help or tips

Thanks Natkirky

Hi Can i please have help simplifying this equation:

(x² - y²)² + 4xy(x+y)²

I am in 1 year at uni however, it's been 4 years since i done maths and i was never great at factorising.

I understand that i am looking for a common factor the solution i have is (x+y)^4 I have tried everything i can think of and can't get this.

Thank you

Hi,

Can someone help me with this complex equation

1/Z + 1/2+i = 1/1+3i?

The answer is  Z=-3 + i

I have tried everything i can think of and can't get this

Thank you

Hi i was wondering if anyone could help me with this question.

Find integers m and n such that 8m + 26n = 2.

I can't make sense of my notes and don't even know how to start.

Thank you

Hi,

Can someone please show me how to work out this equation?  [exp (x+3 ln x)]² 

I have the answer but no working and I can't get to it.

Its the whole equation being raised to 2 that's getting me, can you square exp? If so how does this work.

I might be missing something really silly I'm not great with logs and keep forgetting all the different formulas.

Thank you