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Let f:R to R be a positive increasing fu...

Let `f:R to R` be a positive increasing function with `lim_(x to oo) (f(3x))/(f(x))=1`. Then `lim_(x to oo) (f(2x))/(f(x))=`

A

(3/2)

B

3

C

1

D

(2/3)

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C
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. lim(x rarr oo) (logx^(n)-[x])/([x]), where n in N and [.] denotes the ...

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  2. Let f(a) = g(a) = k and their n^(th) order derivatives exist and are n...

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  3. Let f:R to R be a positive increasing function with lim(x to oo) (f(3x...

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  4. lim(x rarr 0) x^(2). sin (pi/x) is

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  5. If 0 lt x lt y, then lim(n rarroo)(y^(n)+x^(n))^(1/n) is equal to

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  6. The value of lim(x rarr 0) (e^(x)-e^(sinx))/(2 (x-sinx))=

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  7. If f(x) = {((sin(1+[x]))/([x]), for [x] ne 0),(0, for [x] = 0):} , wh...

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  8. If f : R rarr R is defined by f(x) = [x-3]+|x-4| for x in R, then lim(...

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  9. lim(x rarr 0) ((1-e^(x))sin x)/(x^(2)+x^(3)) =

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  10. lim(x rarr 0) (sqrt(1+x)-1)/x =

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  11. If f(x) = [((sin [x])/([x]), [x] ne 0),(0, [x] = 0)], then lim(x rarr ...

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  12. The value of lim(x rarr k^(-)) x -[x], where k is an integer, is

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  13. The value of lim(x rarr 0) (1-cos(1-cosx))/(x^(4)) is

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  14. lim(x rarr 3)[x] =

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  15. lim(x rarr 1) (x^(8)-2x+1)/(x^(4)-2x+1) =

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  16. If f(x) = sqrt((x-sinx)/(x+cos^(2)x)), then lim(x rarr oo) f(x) =

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  17. lim(n rarr oo) (1+(sin) a/n)^(n) equals

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  18. lim(x rarr 0) (4^(x)-1)/(3^(x)-1) =

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  19. The value of lim(n rarr oo){1/1.3+1/3.5+1/5.7+...+1/((2n+1)(2n+3))} is

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  20. The valueof lim(x rarr 0) (e^(ax)-e^(bx))/x is

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