girijanair2010
Answered

 question refers to class 11th maths..chapter Limits and derivatives......We have to find the limt of this qustion....Lim(x-0) (x+1)^5 - 1 / x . I got solution to this qustion on topperlearnign bu i have doubt....

Solution Says - Put x+1 = y so that y -> as x - 0[my question is why do they put x+1 = y ]

                        lim(x-0)   (x+1)^5 - 1 / x = lim(y-1) y^5 -1 / y-1
                                                              lim(y-1) y^5-1^5 / y-1
                                                                           5.1 ^ 5-1
                                                                       =5
                                  



Answer :

If you put x=y in the given equation it would make no change to the equation as y will take place of x only, Thus what you get will be
[tex]lim_{y \to \ 0} [(y+1)^5 -1]/y[/tex] which is same as your given  equation.
For finding a solution to any question the logic is to convert the question into general (predefined forms) which we have already learned.
The asked limit looks alot similar to the formula :
[tex] \lim_{x \to \(a} [x^n-a^n]/x-a [/tex] = [tex]n a^{n-1}[/tex]
So, for converting the above format in this predefined format we put x+1=y
Now [tex] {x \to \(0} \\ {y \to \(1}[/tex] 
So we can write, 
[tex] \lim_{y \to \(1} (y^5-1)/(y-1)[/tex]
Here a=1, n=5 so the solution is [tex]5[1^{5-1}][/tex] = 5
abhishek123
it is common sense that to solve the limits you have to convert the question to a known form which you can solve. to do exactly that you have to do the operation that has been suggested.

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