Recent content by zzmanzz

Homework Statement Hi, this is more of a review question and I'm just looking at solutions of natural cubic spline equations and some will give the cubic spline as: 1. s(x) = a + bx + cx^2 + dx^3 on Wolfram while other pages will give: 2. s(x) = a + b(x - t) + c(x-t)^2 + d(x-t)^3 where...

Homework Statement For the following notation, D \subseteq \{ z | \exists x,y \in S (z = x - y ) \} I'm wondering if S can only have one element, or does the notation imply that | S | > 1 Homework EquationsThe Attempt at a Solution For example, if I have S = \{ 3 \} is z = 3 - 3? Or...

Homework Statement Suppose we have: ## f(x) = x^2 - b ## ## b > 0 ## ## x_0 = b ## And a sequence is defined by: ## x_{i+1} = x_i - \frac{f(x_i)}{f'(x_i) } ## prove ## \forall i \in N ( x_i > 0 ) ## Homework Equations The Attempt at a Solution a)Here I tried solving for ## x_1 ## as...

Thanks for the example - very helpful. I think that f_1 \notin \Omega(f_2) means that f1 is not in the set of functions asymptotically bounded below by f2and implies \forall c_1 > 0 ,n_0, \exists n > n_0 \quad c_1 f_2(n) > f_1(n) In this adjustment of the formula, we say that some n...

Thank you for the response. I think I may have made a mistake in the notation so I went back to the textbook to make sure that everything is accurate for this Big Omega which provides an asymptotic lower bound for functions. 1. \Omega(f_1) = \{ g_1(n) :\exists c_1, \exists n_0 , c_1 > 0...

Homework Statement I usually struggle with proofs and would appreciate some help with the following problem: Prove the following fact: \Omega(f_1) \subseteq \Omega(f_2) iff f_1 \in \Omega(f_2) Homework Equations \Omega(f_1) is the set of functions g s.t. g(n) \geq c f_1(n) where...

Thank you!

Thanks for pointing that out. The value for that should also be between .5 and 1, and with that root, it can be greater than 1?

Homework Statement I was hoping someone could just verify this solution is accurate. p(x) = 0 , x < 0 4x, x < .5 -4x + 4 , .5 <= x < 1 Find CDF and Inverse of the CDF. Homework EquationsThe Attempt at a Solution CDF = 0 , x < 0 2x^2 ...

Thanks so much for your replies and yes, this is a homework question -- but it is not graded. Not sure if that makes a difference. So please roar with me while I try again: A = it will rain tom B = app predicts rain prior probability it will rain tomorrow: P(A) = 1/5 prior probability it...

Hi, I'm not sure whether my understanding of this question is correct: An app predicts rain tomorrow. Recently, it has rained only 73 days each year. When it actually rains, the app correctly forecasts rain 70% of the time. When it does not rain, it incorrectly forecasts rain 30% of the time...

Homework Statement So I thought I knew how to do synthetic division but ran into this problem 4a^4+4a^3-9a^2-4a+16 / (a^2-2) Homework EquationsThe Attempt at a Solution [/B] All the examples I can find don't have a second degree polynomial in the denominator. i.e. they are a-3 or a+2. How...

Thanks for the reply. So, looking back: \cos(n\pi) = (-1)^n \sin(n\pi) = 0 \sin(\frac{n2}{\pi}) = (-1)^{((n-1)/2)} for n odd, 0 for even the sin cancels out though and doesn't matter? \cos(\frac{2n}{\pi}) = \frac{(1+(-1)^n)}{2*(-1)^{n/2}}

you are right. thank you.. i was copying from my notes and might have caried that from the next step. good catch

Homework Statement I got the problem down to: \frac{2}{\pi} \left[ \int_{0}^{\pi/2} \frac{2}{\pi}xsin(nx) dx + \int_{\frac{\pi}{2}}^{\pi} (\frac{-2}{\pi}x+2)sin(nx) dx \right] \frac{4}{\pi^2} \left[ \int_{0}^{\pi/2} xsin(nx) dx + \int_{pi/2}^{\pi} -xsin(nx) dx + \int_{pi/2}^{\pi} \pi...