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!!!!

Question

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!!!!

bharat bajaj · Answer

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

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IIT Delhi

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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!!!!

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!!!!

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