Pn − 1 2 = P0 − 1 2 P2n 1 2 + P1 − 1 2 P2n−1 1 2 + · · · + P2n − 1 2 P0 1 2
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∞
n=0
Pn(cos θ)
n + 1
= log{1 + cosec(θ/2)}, 0 < θ ≤ π
You are given the values p0 = 0 , p1 = 1 and f(p1) = -1 . One interaction of the Secand method using p0 and p1 has been applied to f(x) to obtain p2 Aitken's delta^2 is the used. The result is p3 = 2/3. Determine f(p0)
Consumer Alice is faced with prices (P1, ..., PN)and she has income I. Her value function V (P1,..., PN, I) = -5 and her optimal multiplier X* = 1. Give an estimate for V (P1, .... PN, I + 2). 5. [10 marks]
$$
\begin{array}{l}
\sum_{r=0}^{n} T_{2 r}(x)=\frac{1}{2}\left(1+\frac{1}{\left(1-x^{2}\right)^{1 / 2}} U_{2 n+1}(x)\right) \\
\text { where, } U_{n}(x)=\sin \left(n \cos ^{-1} x\right) \text { and } T_{n}(x)=\cos \left(n \cos ^{-1} x\right)
\end{array}
$$
4. (a) Solve the differential equation (1 − x 2 )y ′′ − 2xy′ + λ(λ + 1)y = 0 using power series centered at 0 , in which λ is a constant. Write your solution as a linear combination of two independent solutions whose coefficients are expressed in terms of λ . Compute the coefficients of each solution up to and including the x 5 term. Without computing them, what is the smallest possible value of the radius of...
4. (a) Solve the differential equation (1 − x 2 )y ′′ − 2xy′ + λ(λ + 1)y = 0 using power series centered at 0 , in which λ is a constant. Write your solution as a linear combination of two independent solutions whose coefficients are expressed in terms of λ . Compute the coefficients of each solution up to and including the x 5 term. Without computing them, what is the smallest possible value of the radius of...
Topology
For all s ε 1-1 1], let P1 (s) = 0 and Pn+1(s) = Pn(s) +--Re) for all n > 1. (b) (i) For every n > 1 and Isl-1, show that 0 < pn(s) sl and Pn(s) Pn+1(s) Conclude that(PJnzi converges uniformly to ρ on [-1,1], where pls) = Isl. (ii)
For all s ε 1-1 1], let P1 (s) = 0 and Pn+1(s) = Pn(s) +--Re) for all n > 1. (b) (i) For every n >...
Let {p0, p1, p2} be a basis for a subspace V of ℙ3, where the pi are given below, and let the inner product for ℙ3 be given by evaluation at 0, 1, 2, 3, so <p,q> = p(0)q(0)+p(1)q(1)+p(2)q(2)+p(3)q(3). Use the Gram-Schmidt process to produce an orthogonal basis {q0, q1, q2} for V and enter the qi below. p0 = x−1 p1 = x2−2x+2 p2 = −3x2+2x q0 = q1 = q2 =
QUESTION 13 Variable count=0 is shared between processes P0 and P1. P0 executes code count++;. P1 executes code count--; P0 and P1 run concurrently, without any synchronization. Each process runs exactly once. What is the value of count after the execution of both processes? 1 0 -1 or 1 -1 -1, 0 or 1 QUESTION 14 Six dining philosophers, fully aware of the potential deadlock (and death of starvation), enumerated their chopsticks 0 through 5 and agreed that a hungry...
A consumer magazine wants to figure out which of two major airlines lost a higher proportion of luggage on international flights. The magazine surveyed Standard Air (population 1) and Down Under airlines (population 2). Standard Air lost 45 out of 600 bags. Down Under airlines lost 30 of 500 bags. Does Standard Air have a higher population proportion of lost bags on international flights? Which of the following is the correct competing hypotheses? a. H0: p = p0, HA: p...