Question

Consider these four functions. Choose the one which will be the greatest as x → ∞. A) h(x) = 3x B) f(x) = x25 C) g(x) = 5x500 D) k(x) = x8 + 8000

Answer 1

For this case what you should know is that all functions tend to infinity when x tends to infinity.
 However, there are functions that grow faster than others.
 In this case, the function that grows fastest is the one with the highest exponent.
 We have then:
 g (x) = 5x ^ 500
 The exponent of 500 makes the function grow to infinity faster than the other functions.
 Answer:
 C) g (x) = 5x500