Recent content by alpha01

we know that cos(x) intersects sin(x) in the interval 0< x< pi/2... but how can i find (x,y) points of this intersection? (without plotting and estimating based of the resultant graph)

it says give your answer "accurate to three decimal places" that is what I am unsure about... that sounds like i can just do one repetition and write the answer to 3 decimal places.. but that sounds too easy (its for my finals, it should be harder i think)

thanks

I had a look but still couldn't figure it out ...it wants the solution to 3 decimal places..

Homework Statement using Newtons method with an initial estimate of x0=2, find the point where the graph f(x)=x3-x-2 crosses the x-axis Homework Equations xi+1 = xi - f(xi)/f'(xi) The Attempt at a Solution Using a function plotter, I know the answer should be around 1.52138...

How do i find the horizontal asymptote for f(x)=xe-x2 thanks for the help.

we have z = 5+2i how do i find the following: |z| z-1 i can do the basic operations (x, /, +, -) with complex numbers but i have no idea where to even start with these 2.

actually i have x=-1 so should be (x+(1-2i))(x+(1+2i))... not (x-(1-2i))(x-(1+2i))

actually.. i just noticed something when i actually went back and wrote it... shouldn't it really be (x+(1-2i))(x+(1+2i))? because x = - 1 is x + 1 = 0 for both solutions so the only thing that should change in the outcomes is the sign in front of the 2i why does one of the factors in your...

thank you logicalTime. It makes perfect sense now.

is this not correct?

there is an example in my notes where the quadratic equation has been used for polynomials with no real solutions. Using the same principal here we have: x = (-2 +- sqrt(-16)) / 2 now, the square root of 16 is 4 so we have x = (-2 +- 4i)/2 = -1 +- 2i and that's how i got my roots.

i jus started in complex numbers today and that's what i came up with.. if someone could please move the thread to the correct place that would be appreciated.. Mark44, Can you please advise how i should go about finding the solution to that part of the question?

x3+4x2+9x+10 finding 1 root and using synthetic division we can factorize to: (x+2)(x2+2x+5) using complex numbers to factorize (x2+2x+5) we have (x+1)(x-2i)(x+2i), and so our final solution is: (x+2)(x+1)(x-2i)(x+2i) is this correct?

i was aware of the definition i=sqrt(-1) but didnt notice it in there. thanks for pointing that out. i am also in aus, i am doing undergrad degree in applied finance at macquarie, its for math130 which is roughly equivalent to 3 unit hsc math.