Finding the limit at infinity?

Question

find the lim as x approaches infinity for 3x^2+20x/(4x^2+9)

also

find the lim as x approaches infinity for 5x-9/(4x^3+1)

How do you calculate limits at infinity?

I'd appreciate any help.

Thank You.

Answer 1

Think about what happens to the fraction 1/x^n as x approaches infinity (n > 0). As the denominator keeps getting bigger the fraction keeps getting smaller. It gets closer and closer to zero.

To solve your problem, you need to do something to it so you have a bunch of terms like 1/x^n. Divide both the numerator and denominator by x^n. You need to figure out what n to use. The n you use should make all but one term in the denominator be in the form 1/x^(something positive) In other words, let n be the highest power of x in the denominator.

You'll be left with only constant terms and 1/x^(something) terms. When you take the limit as x approaches infinity all the 1/x^(something) terms become zero. You'll be left with (something)/(something). This will be your answer.

Answer 2

1) 3/4

2) 0

Ideas: Think of this as finding horizontal asymptotes.

Answer 3

there is no limit