Compare the rates of growth of f(x) = x + sinx and g(x) = x as x approaches infinity.

Question

f(x) grows faster than g(x) as x goes to infinity.
g(x) grows faster than f(x) as x goes to infinity.
f(x) and g(x) grow at the same rate as x goes to infinity.
The rate of growth cannot be determined.

I think it is A because f(x) would grow faster because of the sinx

Answer 1

disagree,
the value of sinx fluctuates between -1 and 1, so as x approaches infinity, adding or subtracting a number between 0 and 1 will be insignificant.
The values of f(x) and g(x) will differ by at most 1
- their rates of growth would vary just be a bit
My pick would be the last one, cannot be determined.

Answer 2

Take the derivative of each to find the rates of growth.

f'(x) = 1 + cos(x)
g'(x) = 1

lim_{x→∞} g'(x) = 1 but
lim_{x→∞} f'(x) does not exist because cos(x) varies between -1 and 1.

Therefore, the rates of growth cannot be compared.

Answer 3

They both grow at the same rate. D is a trick answer.

Answer 4

Thanks Joy :D

Answer 5

geeet dunked on!

Answer 6

f(x) and g(x) grow at the same rate as x goes to infinity is the right answer.