Past sunday i gave a mathematics olympiad exam at IIT Bombay. I was asked a problem in which i had to find limit of problem :
limit x approaches infinity.
there are 2 ways of evaluating this limit.
1) by using the fact that
we get the value of limit as
2) by separating the denominators and using the fact that limit of a sum is the sum of the limits.
And it turns out that the value of limit is 0.
I was confused at this while writing the exam. So I choosed by random.
And I am wondering if I did right decision or not. So I asked here. Please consider explaining me why we get two distinct answers and if my first or second approaches have any errors then please tell me. Thanks