Question

Let f be the function defined by f(x)=2x+3e^(−5x), and let g be a differentiable function with derivative given by g′(x)=1/x+4cos(5x). It is known that limx→∞g(x)=∞. The value of limx→∞f(x)/g(x) is

Answer 1

g(x) = lnx + 4/5 cos(5x) + c
lim(x→∞) f(x) = 2x = ∞
lim(x→∞) g(x) = lnx = ∞
f(x)/g(x) → 2x/lnx = ∞
since polynomials grow faster than logs (or use l'Hôpital's Rule)

Answer 2

oobleck, why are you the way you are man?

Answer 3

1/2