How to find identify the correct substitution for x in a given limit.Is double substitution possible for x like one substituion for root index blank of x and for x.

Asked by royalekawasaki | 13th Jul, 2015, 10:11: PM

Expert Answer:

The substitution in a given limit depends on the expression. We use a substitution which will simplify the given expression. 
For example, to find 
stack l i m with x rightwards arrow 0 below fraction numerator 2 square root of x over denominator 1 plus x end fraction
w e space c a n space u s e space s u b s t i t u t i o n space x equals tan squared theta
w h e n space x rightwards arrow 0 comma space tan squared theta rightwards arrow 0 comma space theta rightwards arrow 0 S o space t h e space l i m i t space b e c o m e s stack l i m with theta rightwards arrow 0 below fraction numerator 2 tan theta over denominator 1 plus tan squared theta end fraction equals stack l i m with theta rightwards arrow 0 below sin 2 theta equals 0
 
But in the same limit we cant use different substitution for sqrt(x) and (x). 
If we can split the limit and write it as lim(x->a) f(x) + g(x) , then for f(x) and g(x) we can use two different substitutions. 
 

Answered by satyajit samal | 14th Jul, 2015, 10:35: AM