Mathematical problem

1. (3 poin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ints each) Fin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ind the values of p for which the followin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ing in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">integrals converge. a) dx x(ln x) p 1 2 ∫ b) dx x(ln x) p 2 ∞ ∫ 2. (3 poin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ints) Determin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ine whether dx ex + e− x −∞ ∞ ∫ converges or diverges. If it converges, fin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ind what it converges to. 3. Consider ln x dx 1 5 ∫ . Use Es ≤ K(b − a) 5 180n 4 . a) (3 poin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ints) Give the maximun error bound for usin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ing Simpson’s Rule to evaluate this in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">integral for n = 6. b) (2 poin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ints) How large must n be so that the Simpson’s Rule estimate is accurate within" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in 0.001? 4. (3 poin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ints) Use Euler’s Method with step size 0.5 to estimate y(2), where y(x) is the solution to the in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">inial value problem y' = x + xy y(0) = 1. 5. (3 poin" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">ints) A population grows at a rate that is proportional to its population. In 2008 (t = 0) , there were 20,000 people present, In 2014, there were 25,000 people present. Write an in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">initial value problem for this situation, solve it, and estimate the population in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in" rel="nofollow">in 2015.