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lim(n->oo)n^(- n^2)((n+1)(n+1/2)(n+1/2^2...

`lim_(n->oo)n^(- n^2)((n+1)(n+1/2)(n+1/2^2)....(n+1/(2^(n-1))))^n`

A

`e`

B

`e^(2)`

C

`e^(3)`

D

`e^(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
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ARIHANT MATHS-LIMITS-Exercise (Single Option Correct Type Questions)
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  3. Let f(x)=lim(nrarroo)1/((3/(pi)tan^(-1)2x)^(2n)+5) then the set of val...

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  4. The integer n for which the lim(x to 0)(cos^(2)x-cosx-e^(x)cosx+e^(x...

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  5. If I(1)=lim(xto 0)sqrt((tan^(-1)x)/x-(sin^(-1)x)/x) and I(2)=lim(xto...

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  6. underset(xto(pi)/(2))(lim)([(x)/(2)])/(log(e)(sinx))([.] denotes great...

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  7. Let a1=1, an=n(a(n-1)+1 for n=2,3,... where Pn=(1+1/a1)(1+1/a2)(1+1/a3...

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  8. If f(x+ y) = f(x) + f(y) for x, y in R and f(1) = 1, then find the val...

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  9. lim(n->oo)n^(- n^2)((n+1)(n+1/2)(n+1/2^2)....(n+1/(2^(n-1))))^n

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  10. If f(x)={((sin[x])/([x]), [x]!=0),(0,[x]=0):} where [.] denotes the ...

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  11. Let f(x)=(|x^(3)-6x^(2)+11x-6|)/(x^(3)-6x^(2)+11x-6) then the number...

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  12. Let the rth term t(r) of a series is given by t(r)=r/(1+r^(2)+r^(4)),...

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  13. The value of lim(ntooo)sum(r=1)^(n)cot^(-1)((r^(3)-r+1/r)/2) is

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  14. Let tan alpha . x + sin alpha · y = alpha and alpha. cosec alpha • x +...

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  15. The polynomial of least degree such that lim(xto0)(1+(x^(2)+f(x))/(x^(...

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  16. If n is a non zero integer and [*] denotes the greatest integer functi...

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  17. The value of lim(xtoa)[sqrt(2-x)+sqrt(1+x)], where a epsilon[0,1/2] an...

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  18. The value of lim(xto0^(+))(-1+sqrt((tanx-sinx)+sqrt((tanx-sinx)+sqrt...

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  19. Evaluate: ("lim")(nvec0)(cos^2(1-cos^2(1-cos^2(cos^2(theta)))))/(s in(...

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  20. The value of lim(ntooo)a(n) when a(n+1)=sqrt(2+a(n)), n=1,2,3,….. is

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