Math Calculators, Lessons and Formulas

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« Limit of a Rational Function
Limits: (lesson 3 of 5)

Limit of Irrational Functions

Example 1:

Multiplying by a unity factor

Limit of a Irrational functions

Solution:

Multiply by 1 in the form of the numerator with a "+" sign substituted for a "-" sign:

Limit of a Irrational functions example

Therefore,

Limit of a Irrational functions solution

Please note in the above examples that, once the limit has been taken, the limit symbol is removed and the fixed point is substituted for x. Prior to that, the limit symbol is needed. When we are doing pure algebra, we leave off the limit symbol to avoid cluttering the math.

Example 2:

Limit of a Irrational functions example

Example 3: Find limit:

Solution:

Here it helps to do a substitution:

Limit of a Irrational functions example

so that we can now write the limit expression as

Limit of a Irrational functions solution

Example 4:

Example 5: Find limit

Solution:

Limit of a Irrational functions