# EVALUATING LIMITS BY RATIONALIZING

Evaluating limits can be done in the following ways.

• Applying the given limit directly. While doing so, sometimes there is a chance to get indeterminant forms.

Some of the indeterminant forms are :

0/0, ∞/∞, ∞∞, 0∞

• After simplification, we can apply the limit.
• After performing rationalization.

Conjugate of √a+b is √a-b

Conjugate of √a+√b is √a-√b

Conjugate of b+√a is b - √a

To perform rationalization, we have to multiply numerator and denominator by the conjugate.

Evaluating the given limits :

Problem 1 :

Solution:

Problem 2 :

Solution:

Problem 3 :

Solution:

Problem 4 :

Solution:

Problem 5 :

Solution:

Problem 6 :

Solution:

Problem 7 :

Solution:

Problem 8 :

Solution:

Problem 9 :

Solution:

Problem 10 :

Solution:

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