Evaluation of limit:
When the provided limit is not in the median form, limit may be calculated by directly using the definition of limit or placing a in place of x if x->a. For example (x+3) =6 Here form is not undefined.
When the form of the provided function is indeterminate, then our motive may be to get rid of the undefined form. After getting rid of the indeterminate form we need the definition of limit or completely put the value. For example
The subsequent techniques are valuable for calculating limits of algebraic function.
Method of factorisation: If f(x) and g(x) are polynomials such that f(a) = g(a) = 0, then (x - a) is a factor of each f(x) and g(x). Now to calculate, we cancel the common factor (x - a) from both the denominator and numerator, and again put x = a in the provided expression. If we take a meaningful number, then the number is the limit of the provided expression otherwise we repeat the method till we get rid of indeterminate form.
Method of rationalisation: If in some limit numerator or denominator involve the radical sign, this process is useful.
Problem: Calculate
Solution:
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