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(5/x). It is known that limx→∞g(x)=∞. The value of limx→∞f(x)/g(x) is

Answer 1

as x→∞, g'(x)→1/ so g(x)→lnx
Logs grow more slowly than polynomials, so
as x→∞, f/g→ x/lnx →∞