Precise Definition of Limits at Infinity...2

Calculus
Section 2.6

See Definition 9 below.

 

for the limit
illustrate Definition 9 by finding a value of N that corresponds to M=100

let function be defined on some interval (a, ∞), then lim(f(x))=∞ as x->∞means that for every positive number M there is corresponding positive number N such that if x>N then f(x)>M

Definition 9:
f(x) is continuous on an interval if it is continuous at every point of the interval

Let M>0 and N=x*ln(x).

Then, for all x>N, we have

sqrt(x*ln(x))>sqrt(N)=sqrt(x*ln(x))=M.

since given M=100, sqrt(x*ln(x))=100
x ln(x) = 10000

since N=x*ln(x), then N=10000

 

Wonderfully-done! I like it.