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The limit underset( theta rarr0 ) ("lim"...

The limit `underset( theta rarr0 ) ("lim") ([ (nsin theta)/( theta) ]+ [ ( n tan theta )/( theta)] ) ,n in N ` is
( where `[ **]` denotes greatest integer function )

A

2n

B

`2n+1`

C

`2n -1`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
C
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MOTION-LIMIT-EXERCISE -1
  1. If [x] denotes the greatest integer le x , then underset( n rarr oo ) ...

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

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

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

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

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

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

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  9. lim(x->0^+)cos^(- 1)(1-x)/(sqrt(x))

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  10. underset( x rarr 0 ) ("lim") [ ( 1-e^(x)) ( sin x )/( |x|)] is equal ...

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  11. Evaluate: underset(hrarr0)("lim")(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(...

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  12. lim(x->0) sin(6x^2)/(lncos(2x^2-x)

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  13. The value of underset( x rarr 0 ) ( "Lim") ( sin ( ln ( 1+ x)))/( ln (...

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  14. underset( x rarr pi //2) ("Lim") ( 2 ^(cos x) - 1)/( x ( x-pi //2))= ...

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  15. lim(x->0)((4^x-1)^3)/(sin(x/p)ln(1+(x^2)/3) is equal to

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  16. The limit underset( x rarr a ) ("Lim") (2 -( a)/(x))^(tan ((pix)/( 2a)...

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  17. underset( x rarr oo) ( "Lim") ((x+ 2)/( x-2))^(x+1)=

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  18. The value of underset( x rarr pi //4) ("Lim") ( 1+[x])^(1//ln( tan x)...

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  19. lim(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x is equal to

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  20. underset( x rarr 0 ) ("lim") ( cos mx )^(n//x^(2))

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