Evaluation of limit Assignment Help

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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 1366_Basic theorems on limits.png(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 1585_Evaluation of limit.png

                                1980_Evaluation of limit1.png 

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 calculate1278_Evaluation of limit2.png, 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 73_Evaluation of limit3.png

Solution:             

                      1232_Evaluation of limit4.png

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