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Calculus
Section 2.6
See Definition 9 below.
Section 2.6
See Definition 9 below.
for the limit View attachment 3333
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