Expert: Bobby Soltani - 3/25/2005

Question
Hi,
I have just purchased the book,Calculus for Dummies,and I found that by limits, it doesn't teach this type of problem: Find the limit as x approaches infinity of [(2^x)/x]. Can you please explain to me how to do these types of problems.(Another example may be: find the limit as x approaches infinity of (x^2)/(2^x).)  

Answer
Hi Jeff,

I can't remember off the top of my head the exact method to solve this problem.  However, from looking at the examples, it is evident that your firt problem approaches positive infinity as x approaches infinity and the second problem approaches zero as x approaches infinity.

The 2^x term grows extremely rapidly.  So, in the first problem, for instance, when x = 20,
f(20) = 52428.8
f(40) = 27 billion

For the second problem, the same thing happens but the large number is in the denominator so it approaches zero.

I hope this helps a little.

Bobby