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Evaluate the limit: ("lim")(nvecoo)cos(p...

Evaluate the limit: `("lim")_(nvecoo)cos(pisqrt(n^2+n))w h e nni sa nin t ege r`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. The value of (lim)(x->0)(sqrt(2)-sqrt(1+cos x))/(sin^2x) is 1/(2sqrt(...

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  2. If a1=1\ a n d\ a(n+1)=(4+3an)/(3+2an),\ ngeq1\ a n d\ if\ (lim)(n->oo...

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  3. Evaluate the limit: ("lim")(nvecoo)cos(pisqrt(n^2+n))w h e nni sa nin ...

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  4. lim(n->oo)prod(r=3)^n(r^3-8)/(r^3+8)

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  5. If [x] denotes the greatest integer less than or equal to x , then eva...

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  6. Let f(x)=[((x^2+3x-1)t a n x)/(x^2+2x)\ if\ x!=0,kif\ x=0 f(x) is cont...

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  7. f(x)=[(sin x+sin5x)/(cos x+cos5x)\ \ if\ x!=-pi/4,k\ if\ x=-pi/4 is co...

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  8. If f(x)=[x+1,\ xlt=1 ,3 -a x^2,\ x >1 is continuous at x=1 then find t...

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  9. What kind of discontinuity the function (cosx)/x h a s\ \ a t\ x=0.

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  10. If f(x)=[(8^x-4^x-2^x+1^2)/(x^2\ ),\ x >0e^xsinx+4x+k ln4,\ xlt=0 is c...

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  11. Let f(x)={(x-1)sin(1/(x-1)), if"x"!="1"0, if"x"="1"} . Then which one ...

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  12. (lim)(x->1)(1-x)tan((pix)/2)\ a. pi/2 b. pi c. 2/pi d. 0

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  13. The value of (lim)(x->pi/2)(int t\ dt)/(sin(2x-pi))integral from pi/...

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  14. The (lim)(x->0)(cos x)^(cotx) is -1 b. 1 c. 0 d. none of these

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  15. The value of a for which the function f(x)=f(x)={((4^x-1)hat3)/(sin(x...

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  16. The function f(x)=[x^2] (where [y] is the greatest integer less tha...

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  17. If f(x)={x e^(-(1/(|x|)+1/x)),\ x!=0 , 0,\ x=0,\ t h e n\ f(x) is a. C...

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  18. Let f(x) = (1-tanx)/(4x-pi), x != (pi)/4, x in [0,(pi)/2]. If f(x) is ...

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  19. The function f(x)=|x|+|x-1| is Continuous at x=1, but not differentiab...

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  20. Let f"":""RvecR be a function defined by f(x)""=""M in""{x""+""1,""...

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