Lim(x>inf)=2000x^4/200x^4= 10
Show that f(x) = x3 and g(x) = 200x3 grow at the same rate.
I only need the 2nd one
x^3 and 200x^3 do not grow at the same rate. They both grow at a rate proportional to x^2, but that is not the same rate.
To understand the limit of a function as x approaches infinity, we can simplify the expression and then evaluate it.
Given the function: f(x) = (2000x^4)/(200x^4)
To simplify this expression, we can cancel out common terms in the numerator and denominator. In this case, both the numerator and denominator have x^4 terms, so they can be canceled out:
f(x) = (2000x^4)/(200x^4) = 2000/200 = 10
Simplifying the expression yields f(x) = 10.
Now, to find the limit of this function as x approaches infinity, we evaluate the function as x becomes larger and larger.
lim(x->∞) f(x) = lim(x->∞) 10 = 10
Therefore, the limit of f(x) as x approaches infinity is 10.