LIMITS OF RATIONAL FUNCTIONS

Rational function is the ratio of two polynomial functions and it is usually represented as

where g(x) ≠ 0.

Consider the following limit of a rational function.

When you evaluate the above the limit of a rational function, you may get one of the following results.

Solved Problems

Evaluate the following limits :

Problem 1 :

Solution :

Problem 2 :

Solution :

Since the evaluation of the given limit is undefined, the limit does not exist. 

Problem 3 :

Solution :

Problem 4 :

Solution :

Since the evaluation of the given limit results indeterminate form 'zero by zero', simplify the rational function and substitute the given limit for x and evaluate.

Problem 5 :

Solution :

Use the following algebraic identity and factor the expression in denominator.

a² - b² = (a + b)(a - b)

Problem 6 :

Solution :

Use the following algebraic identity and factor the expression in denominator.

a³ + b³ = (a + b)(a² - ab + b²)

Problem 7 :

Solution :

Problem 8 :

Solution :

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