Integration techniques and l'hopital's rule

L'Hopital's Rule : use to find indeterminate limits, find derivative of numerator and denominator separately then evaluate limit

L'Hop Regular Indeterminate : (∞/∞), (0×∞), (0/0)

Lim x~>infinity x^1/x : y=x^1/xLny = 1/x ln(x)lim = ln(x)/x= 1/x / 1 = 1/ infinity = 0y = e^0 = 1

Integration by parts formula : ∫udv = uv - ∫vdu , let u = LIPET