Mathematics Challenge Marathon

[jamonwindeyer]

I feel as though my tone was too toxic when I first signed up for these forums.

Anyway, here's another question. I originally wrote it for a treat but it was considered 'too hard'. So I decided to put it here. Warning: It is long.
(Image removed from quote.)

Required knowledge

Preliminary Basic Arithmetic and Algebra, HSC Exponential and Logarithmic Functions, HSC Series, HSC Geometrical Applications of Differentiation

Hint for d)

It says to use part b). But avoiding using the sum of a G.P. MAY prove useful.

OMG IT HAS SURFACED!!!

[Rathin]

Whenever I see a finincial maths series question I get a little depressed lol..so glad I'm not sitting the 2u hsc

[wyzard]

I feel as though my tone was too toxic when I first signed up for these forums.

Anyway, here's another question. I originally wrote it for a treat but it was considered 'too hard'. So I decided to put it here. Warning: It is long.
(Image removed from quote.)

Required knowledge

Preliminary Basic Arithmetic and Algebra, HSC Exponential and Logarithmic Functions, HSC Series, HSC Geometrical Applications of Differentiation

Hint for d)

It says to use part b). But avoiding using the sum of a G.P. MAY prove useful.

Here's my train of thoughts.

"Yeap first question showing some stuff in calculus... pretty straight forward... Next question financial math...yeah nah  "

[RuiAce]

Remember, you can't log a negative number (until you do complex analysis).

[RuiAce]

A nice work-around given the even power which I didn't anticipate. It wouldn't be "too" valid if the power ended up being odd.

Also, I very much prefer an exact form; not a calculator value

[pikachu975]

Remember, you can't log a negative number (until you do complex analysis).

= [30ln|x|] from -100 to -10
= 30(ln10-ln100)
= 30ln(1/10)

Is this valid considering you put absolute values when integrating to log?

[RuiAce]

= [30ln|x|] from -100 to -10
= 30(ln10-ln100)
= 30ln(1/10)

Is this valid considering you put absolute values when integrating to log?

Pretty much yeah.

[RuiAce]

[georgiia]

I understand this graphically, but I'm afraid I don't get the maths behind it :/

[RuiAce]

[georgiia]

Yeah I understand that, what I don't get is why it's a cubic. I understand visually, but I can't prove what makes it not be a positive parabola above a negative one.

[RuiAce]

Yeah I understand that, what I don't get is why it's a cubic. I understand visually, but I can't prove what makes it not be a positive parabola above a negative one.

It actually ain't a cubic at all

Being two separate halves of a parabola might make it appear as though it were a cubic, but it most certainly is not a cubic.

[georgiia]

It actually ain't a cubic at all

Being two separate halves of a parabola might make it appear as though it were a cubic, but it most certainly is not a cubic.

I meant it looks like one ahahaha!
How does this work? do you not post the next question until the previous one is completed?

[RuiAce]

Also, why it's half a 'positive' parabola and half a 'negative' parabola is really just a consequence out of the algebra. Basically you ended up with a piece-wise defined function

I meant it looks like one ahahaha!
How does this work? do you not post the next question until the previous one is completed?

Used to be like that, but now I don't care too much and I'm happy for questions to be thrown in whenever someone feels like it.

[georgiia]

For Q.a did you mean

a^x ln(x) ?

Maybe I'm just doing something wrong?