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Evaluate ("lim")(nvecoo){cos(x/2)cos(x/4...

Evaluate `("lim")_(nvecoo){cos(x/2)cos(x/4)cos(x/8) cos(x/(2^n))}`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Evaluate the following limit : (lim)(x->0)((4^x-1)^3)/(sin((x^2)/4)l...

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  2. Evaluate underset(xto0)lim(sinx^(0))/(x).

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  3. Evaluate ("lim")(nvecoo){cos(x/2)cos(x/4)cos(x/8) cos(x/(2^n))}

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  4. Evaluate: ("lim")(hvec0)(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(sqrt(3)h(...

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  5. Evaluate the following limit : (lim)(x->oo)((1-cos2x)sin5x)/(x^2sin3...

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  6. Evaluate the following limit : (lim)(alpha->beta)[(sin^2alpha-sin^2b...

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  7. Evaluate the following limit : (lim)(x->0)((a^x+b^x+c^x)/3),\ (a , ...

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  8. Evaluate the following limit (lim)(x->oo)((3x-4)/(3x+2))^((x+1)/3)

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  9. Evaluate the following limit (lim)(x->oo)((x+3)/(x+1))^(x+1)

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  10. Evaluate the following limit (lim)(x->oo)(1+a x)^(1/x)

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  11. Evaluate the following limit (lim)(x->oo)(1-4/(x-1))^(3x-1)

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  12. Evaluate the following limit (lim)(x->pi/2)(sin x)^(tanx)

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  13. Find the values of a\ &\ b : (lim)(x->oo)[(x^2+1)/(x+1)-a x-b]=0

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  14. lim(x rarr oo) (sqrt(x^2-x+1)-a x-b)=0, then a+b=

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  15. If lim(x -> oo) (1 + a/x + b/x^2)^(2x)= e^2 then the values of a and ...

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  16. F(x) is the function such that (lim)(x->0)(f(x))/x=1\ a n d\ (lim)(x...

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  17. If Sn=sum(k=1)^n ak and lim(n->oo)an=a , then lim(n->oo)(S(n+1)-Sn)/sq...

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  18. (lim)(x->oo)(logx^n-[x])/([x]),\ n in N ,\ ([x]\ d e not e s\ t h e\ ...

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

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  20. If (lim)(x->0)(log(3+x)-"log"(3-x))/(x^2-9)="k", then the value of...

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