IDY in < oo and lim - Yn < 0o. Prove that lim,+ 1. Let In > 0. Yn > 0 such that lim,- Yn) < lim,-- In lim,+ Yn: i tn < oo and lim yn < . Prove that lim. In 1. Let In 20, yn 0 such that lim Yn) < limn+In lim + Yr
Let f(x) be an integrable function such that 1 -4 -4 and 1. 2 Compute the following integrals. Number => [f(e) de » L, (+37(e) +2) de Number c) Se f(a) de = Number
in a laurent series valid (z-2) (1+2) 2+11 > 2
Given the logistic map Xn+1 = run(1 – Xn) with r > 0. Show the 2-cycle is stable for 3 <r <1+V6.
2. a) Solve the initial value problem dy 1 dx 1+2x y -2x+1:y(2)-5 b) Explain why this solution is defined for all x >-
Linear algebra please prove and write neatly Any set of m vectors in R™ is linearly dependent if m>n
13. Write out a synthesis for each of the following transformations. ОН > NH2 olone oo Q-0 > OH
Problem 1. Let X be a contiuous random variable with probability density 2T f0SS Let A be the event that X > 1/2. Compute EXA) and Var(XA).
(1 point) Find the inverse Laplace transform of 2s + 9 $2 + 23 S> 0 y(t) =
(b) Show that if lim sn oo and lim tn > -oo, then lim(sn + tn) 1 +oo.