Question

Show how to compute the following limits algebraically: lim(x)->infinity (4x^4-2x^2+3)/(10x^4-50); Lim (n)->infinity[n(n+1)(2n+1)/6]*[27/n^3]

Answer 1

(4x^4-2x^2+3)/(10x^4-50) = ((1/x^4)(4x^4-2x^2+3))/((1/x^4)(10x^4-50))=
(4-(2/x^2) + (3/x^4))/(10-(50/x^4))
lim x-> infinity ((4-(2/x^2)+(3/x^4))/(10-(50/x^4))= (4-2/infinity+3/infinity)/(10-50/infinity) = 4/10 = 2/5

Answer 2

Do the same thing for the second one, first just distribute everything to its expanded form.