Question

Estimate the limit numerically

lim x→(− Infinity)

(x^4 − 4,000x^3)/
(4x^4 + 9,000)

Answer 1

anything? guys i have no idea how to do this one

Answer 2

as x goes to infinity, the cubed x on top becomes irrelevant, and so does the 9000 in the bottom, plug huge numbers into your calculator & you'll see the result getting closer to 1/4, because the 4th powers blow everything else away when x gets huge. Formally, you divde everything by the largest power of x, so the cubed term becomes 4000/x which goes to 0, and the constant on the bottom becomes 9000/(x^4) which goes to 0 as well, with both powers of 4 in x becoming constants when divided - that's what your'e left with.