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underset( x rarr0 ) ("lim") (sin [cos x ...

`underset( x rarr0 ) ("lim") (sin [cos x ])/( 1+[cos x ] ) `
( where {x} denotes fractional part function )

A

2

B

1

C

0

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
C
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MOTION-LIMIT-EXERCISE -1
  1. lim(x -> 0)[sin[x-3]/([x-3])] where [.] denotes greatest integer funct...

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  2. Given a real valued function f such that f(x)={tan^2[x]/(x^2-[x]^2) ,...

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  3. underset( x rarr0 ) ("lim") (sin [cos x ])/( 1+[cos x ] ) ( where ...

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  4. Lim(x rarr 0^+) ((pi/2-cot^(-1){x})x)/("sgn"x-cosx) (where {.} and sgn...

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  5. underset( x rarroo ) ("lim") sec^(-1) ((x)/( x+1)) =

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  6. If f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", ...

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  7. If f( 2010) = pi //2, f(2x) = f(x) AA x in R and f(x) is continuous f...

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  8. underset( n rarr oo) ( "Lim") ( -3n + (-1)^(n))/(4n-(-1)^(n)) is

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  9. lim(xto oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greate...

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  10. Limit(n->oo) {(1+x) (1+x^2)(1+x^4).......(1+x^(2^n))}= if |x|<1 has th...

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  11. The graph of the function f(x) = underset( t rarr 0 ) ("Lim") ((2x)/(p...

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  12. Let f(x)=(loge(x^2+e^x))/(loge(x^4+e^2x)). If lim(xto oo) f(x)=l and l...

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  13. If [x] denotes the greatest integer le x , then underset( n rarr oo ) ...

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  14. lim(n->oo) 1/sqrt(n^2)+1/sqrt(n^2+1)+1/sqrt(n^2+2)+.....1/sqrt(n^2+2n)...

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  15. The limit underset( theta rarr0 ) ("lim") ([ (nsin theta)/( theta) ]+ ...

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  16. lim(x->-oo) {x^2*sin(1/x)}/sqrt(9x^2+x+1) is equal to

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  17. lim(x->oo)(x^2sin(1/x)+x+1)/(x^2+x+1) is equal to

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  18. Evaluate: ("lim")(nvecoo)ncos(pi/(4n))sin(pi/(4n)) where (x , y)vec(0...

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  19. lim(x->pi/2) ((1-tan(x/2))(1-sinx))/((1+tan(x/2))((pi-2x)^3))

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  20. The limit underset( x rarr0 ) ( "lim") ( 1- cos x sqrt( cos 2x))/( x^(...

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