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If lim(xto oo)(n.3^(n))/(n.(x-1)^(n)+n.3...

If `lim_(xto oo)(n.3^(n))/(n.(x-1)^(n)+n.3^(n+1)-3^(n))=1/3`, the number of the integral values of x is ………..

A

3

B

4

C

5

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-LIMITS-Exercise (Single Option Correct Type Questions)
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  2. lim x→π/4 (4sqrt(2)-(cosx+sinx)^5)/(1−sin2x) is equal to

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  3. If lim(xto oo)(n.3^(n))/(n.(x-1)^(n)+n.3^(n+1)-3^(n))=1/3, the number ...

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  4. Let f(x)=underset(ntooo)lim(1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the...

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  5. Find the integral value of n for which ("lim")(xvec0)(cos^2x-cosx-e^x...

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  6. Find dy/dx if x^7-e^x=siny

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

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  8. If tn=1/4(n+2)(n+3) for n=1,2,3, , then 1/(t1)+1/(t2)+1/(t3)++1/(t(20...

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  9. 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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  10. Evaluate underset(ntooo)limn^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))......

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  11. If f(x)={("sin"[x])/([x]),for[x]!=0, 0,for[x]=0,where [x] denotes the...

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  12. Evaluate: lim(xto2)(x^3-6x^2+11 x-6)/(x^2-6x+8)

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  13. Let r^(th) term t (r) of a series if given by t (c ) = (r )/(1+r^(2) +...

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

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  15. Let xtan alpha + ysin alpha= alpha and xalpha cosec alpha + ycosalpha...

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

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

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  18. The value of lim(xtoa)[sqrt(2-x)], where a in[0,1/2] and [.] denotes t...

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  19. Evaluate: lim(thetato0)(cos^2(1-cos^2(1-cos^2(1-cos^2(theta)))))/(sin(...

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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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