Let f:R->R be a +ve increasing function with lim x->infinity f(3x)/f(x) = 1.

Then lim x->infinity f(2x)/f(x) =

(a) 3/2

(b) 3

(c) 1

(d) 2/3

Exlain the procedure also. Plz!!!!

The key here is that regardless of what a is, ax-> infinity as x ->infinity. If you want to think of it in terms of y-intercepts, you can even if f isn't a polynomial. Multiplying the independent variable by a constant a stretches or compresses the graph in the horizontal direction, but it doesn't change the location of the y-intercept.
Hence, the limit would be the same that is 1.
C) is the answer
Thanks & Regards
Bharat Bajaj

askiitian faculty

IIT Delhi