# Posts by Aoi

Total # Posts: 13

maths...
This is the entire question: A curve has the equation y=(x+2)√(x-1). i)Show that dy/dx = kx/√(x-1) and find k ii)Hence, evaluate limit 2 to 5 ∫ kx/√(x-1)dx My answer: first part, i have already shown, and k is equals to 3/2 I don't get the second ...

maths...
Differentiate ln [x+√(x^2+1)] with respect to x hence evaluate limit 0 to 1 ∫ 1/√(x^2+1) dx _________________________________________ Use the identity cos3x=4cos^3x-3cosx, find ∫cos^3x dx * Is there a printing error in the question? the limit is from pi...

Integration?
given that y=Ae^kx, where A and k are constants, find an expression for dy/dx. Hence find the value of k and of A for which dy/dx - 3y = 4e^2x okay, i know the first part is dy/dx=Ake^kx but how do i do the second part? find A and k?

Maths integration
Please help! These 2 questions are very similar, and i tried to do completing square method, but i cant get the correct answer! I'm trying to get the dy/dx to be a complete square thingy to show that the value is always greater or equal to 0. 1. Show that the function f(x...

Polynomials help
Hello, this is a question which i don't know how to do. Find the value of k for which a-3b is a factor of a^4-7a^2b^2 + kb^4 Hence, for this value of k, factorise a^4 - 7a^2b^2 + kb^4 completely. I tried to do long division for the question, but couldnt. Is there any other...

how do i do division?
(a^4 - 7a^2b^2 + kb^4) ÷ (a-3b) I'm not sure how to divide this by long division or otherwise...

alpha beta identities?
I read on an assessment book that a^3-b^3 = (a-b)[(a-b)^2-ab] Can someone tell me how is a^3-b^3 converted into (a-b)[(a-b)^2-ab]? Same for this: a^3 + b^3 = (a+b)[(a+b)^2-3ab] how do i get this??

POLYNOMIALS
There's a bit of calculation mistakes there, but thanks, i know how to do it now!!!! XD

POLYNOMIALS
The cubic polynomial f(x) is such that the coefficient of x^3 is -1. and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x)has a remainder of 8 when divided by (x-3), find the value of k. okay, this is what i did: -x^3 + bx^2 + cx + d = (x-1)(x-2)(x-k) f(3)=8 -...

POLYNOMIALS
I'm really sorry, i'm preparing for O levels, so i have a lot of maths questions to ask... please excuse me... Question: Find the value of k for which a-3b is a factor of a^4 - 7a^2b^2 + kb^4. Hence, factorise completely. How do i even find k??? Please help thankyou!

POLYNOMIALS
For the previous part, this was how i got the answer: f(x) = (x-1)(x-k)(x-k^2) = Q(x)(2-x)+7 Let x=2, so (2-k)(2-k^2)=7, and i get the answer, But there is another part to this question which i don't understand... please help:D it says: Hence, find a value of k and show ...

POLYNOMIALS
ok... i know how to do this question already! :D

POLYNOMIALS
ok, this might be a bit torturous, but if anyone is patient enough and help me with my working, i'd REALLY APPRECIATE IT!!!! Question: The cubic polynomial f(x) is such that the coefficient of x^3 is 1 and the roots of f(x)=0 are 1, k, and k^2. IT is given that f(x) has a ...