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

`lim_(x rarr 0) x^(2). sin (pi/x)` is

A

1

B

0

C

non existent

D

`oo`

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  3. lim(x rarr 0) x^(2). sin (pi/x) is

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. If S(1) = sumn, S(2) = sumn^(2), S(3) = sumn^(3) then lim(n rarr oo) (...

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