CK12 Calculus - Single Variable

Let’s applytheserulesto help us find limits.
Example 11

Find.
Solution
We coulduse L’Hôpital’s rule or we coulduse someof the rulesin the precedingtheorem.Let’s use the
rulesin the theorem.Divideboth the numeratorand denominatorby the highestpowerofnin the expression
and usingrulesfrom the theorem,we find the limit:

Dividingboth numeratorand denominatorbyn

Simplifying

Applyingthe divisionrule for limits.

Applyingthe rule for the limit of a sum to the denominator

Evaluatingthe limits
Example 12

Find.
Solution

Applyingthe rule for the differenceof two limits

Applyingthe rule for the limit of c timesa limit
Evaluatingthe limits
As with limitsof functions,thereis a Sandwich/SqueezeTheoremfor the limitsof sequences.

Sandwich/SqueezeTheoremLet {an}, {bn} and {cn} be sequences.LetNbe a positivein-

teger. Supposecnis a sequencesuchthatan≤cn≤bnfor alln≥N. Supposealso that

. Then.