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Evaluate underset(xto2)limsin(e^(x-2)-1)...

Evaluate `underset(xto2)limsin(e^(x-2)-1)/(log(x-1))`

A

`-2`

B

`-1`

C

`0`

D

1

Text Solution

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The correct Answer is:
D
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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL -1
  1. Evaluate: (lim)(x->e)(logx-1)/(x-e)

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  2. Evaluate: ("lim")(xvec0)((a^x+b^x+c^x)/3);(a , b , c >0)

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  3. Evaluate underset(xto2)limsin(e^(x-2)-1)/(log(x-1))

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  4. The value of lim(xto0)(x cosx-log(1+x))/(x^(2)) is

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  5. If x gt0 and g is bounded function then lim(ntooo)(f(x)e^(nx)+g(x))/(e...

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  6. The integer n for which ("lim")(xvec0)((cosx-1)(cosx-ehatx)/(x^n) is f...

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  7. If lim(xtooo)(1+a/x+b/(x^(2)))^(2x)=e^2 then values of a and b are

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  8. If lim(xto0)({(a-n)nx-tanx}sin nx)/(x^(2))=0, where n is non zero real...

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  9. Find the values of a and b in order that underset(xto0)lim(x(1+acosx...

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  10. Evaluate underset(xto0)lim(sin[cosx])/(1+[cosx]) ([.] denotes the grea...

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  11. lim (xto (pi)/(3 )) (sin ((pi)/(3)-x))/( 2 cos x-1) is equal to:

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  12. lim(x->1) (x-1){x}. where {.) denotes the fractional part, is equal to...

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  13. Let f(x)={(x^2,x notin Z),((k(x^2-4))/(2-x),x notinZ):} Then, lim(xt...

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  14. If f(x)={("sin"(pix)/2,, x lt1),(4x-3,,1lexle2),(log2(2x^(2)-4),,2ltxl...

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  15. If f(x) = {{:(x((e^(1//x) - e^(-1//x))/(e^(1//x)+e^(1//x)))",",x ne 0)...

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  16. If f(x)=(4+sin2x+a sinx+Bcosx)/(x^(2)) for x!=0 is continuous at x=0, ...

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  17. If f(x)=(sin3x+Asin2x+Bsinx)/(x^(5)) forx!=0 is continuous at x=0, the...

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  18. If f(x)={((a^(2[x]+{x})-1)"/ "(2[x]+{x}),x!=0),(log(e)a,x=0):} Then ...

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  19. Let [] donots the greatest integer function and f (x)= [tan ^(2) x], t...

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  20. f(x)=[tan^(-1)x] where [.] denotes the greatest integer function, is d...

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