For f(x)=(3x^2-5x+2)/(2x^2-6) complete the statements.

Question

f(x)->_________ as x->-infinity
f(x)->_________ as x->infinity

In the blanks, I say for the first one infinity then -infinity for the second one.

Answer 1

use an intuitive approach.
as x becomes "very large" your numerator is dominated by the 3x^2 term and your denominator is dominated by the 2x^2 term, the other terms become less and less significant as x gets bigger

so your function approaches f(x) = 3x^2/2x^2 = 3/2

so the limit is 3/2