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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!!!!

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
6 years ago
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

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