Let f : R\rightarrow R be a positive increasing function with \lim_{x\rightarrow \infty }\frac{f(3x)}{f(x)}=1.\; Then\; \lim_{x\rightarrow \infty }\frac{f(2x)}{f(x)}=

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  • Option 4)

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Answers (1)
P Plabita

As we learnt in

Evaluation of limits : (algebraic limits) : (Method of direct substitution) -

\lim_{x\rightarrow a}f(x)\:defines\:by\:direct\:x=a


ex: \:\lim_{x\rightarrow 1}\:\frac{x^{2}+x+1}{x^{2}+x-1}=3

- wherein

Means at  x = a  f(x) defined.

 

 

 

 Since f(x) is increasing function so that 

\lim_{n\rightarrow \infty}f(x)=\lim_{n\rightarrow \infty}f(2x)=\lim_{n\rightarrow \infty}f(3x)

\lim_{n\rightarrow \infty} \frac{f(2x)}{f(x)}=1

 

 


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Option 2)

2/3

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Option 3)

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Option 4)

3

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