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Factorisation Method to Solve Limits

Here you will learn what is the factorisation method to solve limits with examples.

Let’s begin –

Factorisation Method to Solve Limits

Consider the following limit :

limxa f(x)g(x)

If by substituting x = a, f(x)g(x), reduces to the form 00, then (x – a) is a factor of f(x) and g(x) both.

So, we first factorize f(x) and g(x) and then cancel the common factor to evaluate the limit.

Also Read : How to Solve Indeterminate Forms of Limits

Following algorithm may be used to evaluate the limit by factorisation method.

Algorithm :

1). Obtain the problem, say, limxa f(x)g(x), where limxa f(x) = 0 and limxa g(x) = 0.

2). Factorize f(x) and g(x).

3). Cancel out the common factor.

4). Use direct substitution method to obtain the limit.

Example : Evaluate : limx2 x25x+6x24.

Solution : When x = 2 the expression x25x+6x24 assumes the indeterminate form 00.

Therefore, (x – 2) is a common factor in numerator and denominator.

Factorising the numerator and denominator, we have

limx2 x25x+6x24 = limx2 (x2)(x3)(x+2)(x2)

= limx2 x3x+2 = 232+2 = 14

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