Simpler way to find assymptotes

[Sarita Math]

Please read this note. This is the procedure to find assymptotes for algebraic curves, which is described in "Differential Calculus" by Ghosh & Maity.

It contains two solved problems to make you understand the procedure clearly. Read it carefully.

[Veerendra Singh]

mam i wanted to ask this question.

[Sarita Math]

 is an increasing function of x.

Now applying Taylor's theorem in the following intervals respectively

,

and retaining the first two terms, we get,

 for some 

 for some .

 

adding the above two equations and dividing by 2, we get,

Clearly,   and  is increasing, therefore,  and  always.

Therefore. and thus we get our required result,