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The value of lim(ntooo) [(2n)/(2n^(2)-1)...

The value of `lim_(ntooo) [(2n)/(2n^(2)-1)"cos"(n+1)/(2n+1)-(n)/(1-2n).(n)/(n^(2)+1)]` is

A

5

B

6

C

7

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(ntooo)lim[(2)/(2-(1)/(n^(2))).(1)/(n)cos((1+1//n)/(2-1//n))-(1)/(((1)/(n)-2)).(1)/((1+(1)/(n^(2)))).(1)/(n)]`
`=underset(ntooo)lim(1)/(n)[(2)/(2-(1)/(n^(2))).cos((1+(1)/(n))/(2-(1)/(n)))-(1)/(((1)/(n)-2)).(1)/((1+(1)/(n^(2))))]`
`=0xx[(2)/(2)xx"cos"(1)/(2)+(1)/(2)xx(1)/(1)]=0`.
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CENGAGE-LIMITS-Exercise (Single)
  1. Let f(x)=lim(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). Then the set of...

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  2. f(x)=("ln"(x^(2)+e^(x)))/("ln"(x^(4)+e^(2x))). Then lim(x to oo) f(x) ...

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  3. The value of lim(ntooo) [(2n)/(2n^(2)-1)"cos"(n+1)/(2n+1)-(n)/(1-2n).(...

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  4. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/...

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  5. lim(xto1) (xsin(x-[x]))/(x-1), where [.] denotes the greatest integer ...

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  6. lim(xtooo) (x^(2)"tan"(1)/(x))/(sqrt(8x^(2)+7x+1)) is equal to

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  7. lim(xto0) (x^(a)sin^(b)x)/(sin(x^(c))), where a,b,c inR~{0}, exists an...

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  8. lim(xto0) (x^(4)(cot^(4)x-cot^(2)x+1))/((tan^(4)x-tan^(2)x+1)) is equa...

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  9. lim(xto1) (1-x^(2))/(sin2pix) is equal to

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  10. lim(xto0) (1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to

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  11. lim(yto0) ((x+y)sec(x+y)-xsecx)/(y) is equal to

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  12. lim(xto1) (1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

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  13. lim(ntooo) sum(x=1)^(20)cos^(2n)(x-10) is equal to

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  14. lim(xto-1) ((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/(x+1)^(2)) is...

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  15. lim(xtooo) {(x+5)tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to

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  16. The value of lim(xto0) ([(100x)/(sinx)]+[(99sinx)/(x)]) (where [.] rep...

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  17. The value of lim(xtoa) sqrt(a^(2)-x^(2))"cot"(pi)/(2)sqrt((a-x)/(a+x))...

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  18. lim(xto0) [min(y^(2)-4y+11)(sinx)/(x)] (where [.] denotes the greatest...

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  19. The value of lim(xto0) (1-(cosx)sqrt(cos2x))/(x^(2)) is

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  20. lim(xtooo) (1)/(x+1)tan((pix+1)/(2x+2)) is equal to

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