# Calculate the following limits or explain why they do not exist:?

a) limit as x approaches infinity

(x^3+2x+9) / (x+1)(x^2-5x+1)

b) limit as x approaches infinity

(x^2+3x+5/x+1 - x^2-1/x-1)

c) limit as x approaches (-3)

x^2+9/x+3

Relevance

a) 1. If you multiply out the bottom, you get a x^3. Since the limit is going to infinity, the x^3 on the top and bottom are basically all that matter for computing the limit because it's the biggest term-- you might as well have (x^3)/(x^3). That's 1, and so is the limit.

b) Use L'Hopital's rule, but if you don't know that just say it doesn't exist. If you divide both fractions, you'll end up with an x in each, and for the same reason as above, you get infinity - infinity. That's an indeterminate form, so use L'Hopital's rule.

c) Infinity, or DNE. If you substitute numbers reeeeally close to -3 for x, like -2.9999, you end up with a really small number in the denominator, like 0.000001 or so, and anything divided by something that small is essentially infinity.

Source(s): Math
• Anonymous
4 years ago

a)Lim x------>one million (x-one million)(x+3)/(x-one million)(x+one million)=Lim x---->one million 4/2=2 ======================================... b) 2/4=one million/2 ===================================== c) =0 ================================ Lim +00x^one million/2/x=0 God bless you.