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 :
limx→a 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, limx→a f(x)g(x), where limx→a f(x) = 0 and limx→a 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 : limx→2 x2–5x+6x2–4.
Solution : When x = 2 the expression x2–5x+6x2–4 assumes the indeterminate form 00.
Therefore, (x – 2) is a common factor in numerator and denominator.
Factorising the numerator and denominator, we have
limx→2 x2–5x+6x2–4 = limx→2 (x–2)(x–3)(x+2)(x–2)
= limx→2 x–3x+2 = 2–32+2 = −14