5. Show that if an >0 and an is convegent, then ln(1 + an) is convergent.
Given the logistic map Xn+1 = run(1 – Xn) with r > 0. Show the 2-cycle is stable for 3 <r <1+V6.
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
Show the resistance looking into the base ro= 0 PA + B + 1)RE >RE (b)
2. Show that for > 0, we have x4 + IV
5. Let S be a non-empty bounded subset of R. If a > 0, show that sup (aS) = a sup S where aS = {as : s E S}. Let c = sup S, show ac = sup (aS). This is done by showing: (a) ac is an upper bound of aS. (b) If y is another upper bound of aS then ac < 7. Both are done using definitions and the fact that c=sup S.
check if e-1/4/ f(x) if x > 0 if x < 0 is differentiable at 0.
PLEASE HELP WITH PROOF!! 8. Let an > 0 for all n in 1. Show that if an converges, then Ĉ vanın converges. [Hint: Expand [van - (1/n)]2.) N =
Solve the initial value problem ry' + xy = 1, > 0 y(1) = 2.
gen. • solution of (1) 2² y +3ny -15y =o) z>o (2) 2 By dy - ln x=0 x 20 x azu
All work please Evaluate: SỐ 9(x) dx, where g(x) = x2 for x 5 2 = 5 + x for x > 2 Find the average value of y = 4x3 + 2x over the interval [–2, 1]