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lim(x->oo) 2(sqrt(25x^2+x)-5x) is:...

`lim_(x->oo) 2(sqrt(25x^2+x)-5x)` is:

A

`lim_(xto0) (2x-log _(e) (1+x)^(2))/(5x ^(2))`

B

`lim _(x to 0) (e ^(-x)-1+x)/(x ^(2))`

C

` lim _(x to 0) (2(1-cos x ^(2)))/(5x^(4))`

D

`lim (xto0) (sin ""(pi)/(5 ))/(x)`

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The correct Answer is:
A, C, D
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VIKAS GUPTA (BLACK BOOK)-LIMIT-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. if lim(x->0)(ptanqx^2-3cos^2x+4)^(1/(3x^2))=e^(5/3)

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  2. lim(x->oo) 2(sqrt(25x^2+x)-5x) is:

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  3. Let lim (xtooo) (2 ^(x) +a ^(x) +e ^(x))^(1//x)=L which of the follow...

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  4. Let tan alpha . x + sin alpha · y = alpha and alpha. cosec alpha • x +...

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  5. Let f:R->[-1, 1] be defined as f(x) = cos(sin x), then which of the fo...

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  6. Let f (x) =x + sqrt(x^(2) +2x) and g (x) = sqrt(x^(2) +2x)-x, then:

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  7. Which of the following limits does not exist ?(a) lim(x->oo) cosec^(-1...

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  8. If f(x)=(lim)(nvecoo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1))) where ...

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  9. Let f:R->R;f(x)={(-1)^n if x=1/(2^(2^n)), n=1,2,3.......... and 0 othe...

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  10. If lim(x->a) f(x) = lim(x->a) [f(x)] ([.] denotes the greatest intege...

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  11. let f(x)=(cos^-1(1-{x})sin^-1(1-{x}))/sqrt(2{x}(1-{x})) where {x} deno...

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  12. lim(x->0) (sin(sinx)-sinx)/(ax^3+bx^5+c)=-1/12 then

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  13. If f (x) = lim ( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of...

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  14. lim(n->oo)cos^2(pi(3sqrt(n^3+n^2+2n)-n)) where n is an integer,equals

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  15. If alpha,beta in (-pi/2,0) such that (sin alpha+sinbeta)+(sinalpha)/(s...

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  16. Let f(x)={|x-2|+a^2-6a+9, x < 2 and 5-2x, x >= 2 If lim(x->2) [f(x)] e...

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  17. A circular disk of unit radius is filled with a number of smaller circ...

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  18. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

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  19. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

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  20. A certain function f(x) has the property that f(3x)=alpha f(x) for all...

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