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("lim")(nvecoo)(n(2n+1)^2)/((n+2)(n^2+3n...

`("lim")_(nvecoo)(n(2n+1)^2)/((n+2)(n^2+3n-1))i se q u a lto` 0 (b) 2 (c) 4 (d) `oo`

A

1

B

0

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(ntooo)lim(n(2n+1)^(2))/((n+2)(n^(2)+3n-1))=underset(ntooo)lim((2+(1)/(n))^(2))/((1+(2)/(n))(1+(3)/(n)-(1)/(n^(2))))`
`=((2+0)^(2))/((1+0)(1+0+0))=4`
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CENGAGE-LIMITS-Exercise (Single)
  1. evaluate (i) underset(xtooo)limsec^(-1)((x)/(sinx))" and "(ii) underse...

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  2. lim(x to oo )((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2)) is equal to

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  3. ("lim")(nvecoo)(n(2n+1)^2)/((n+2)(n^2+3n-1))i se q u a lto 0 (b) 2...

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  4. ("lim")(xvecoo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45))i se q u a lto 16 (...

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  5. lim(xtooo) [sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to

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  6. about to only mathematics

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  7. lim(xtooo) ((x+1)^(10)+(x+2)^(10)+...+(x+100)^(10))/(x^(10)+10^(10)) i...

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  8. ("lim")(xvecoo)(2sqrt(x)+3sqrt(x)+4sqrt(x)+...+nsqrt(n))/(sqrt((2x-3))...

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  9. If("lim")(xvecoo)(n .3^n)/(n(x-2)^n+n .3^(n+1)-3^n)=1/3, t h e nt h e ...

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  10. lim(ntooo) n^(2)(x^(1//n)-x^(1//(n+1))),xgt0, is equal to

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  11. Let f(x)=("lim")(xvecoo)1/((3/pitan^(-1)2x)^(2n)+5)dot Then the set of...

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

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  13. The value of ("lim")(xvecoo)[(2n)/(2n^2)cos(n+1)/(2n-1)-n/(1-2n)dot(n(...

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  14. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)...

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  15. ("lim")(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest ...

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

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  17. ("lim")(xvec0)(x^asin^b x)/(sin(x^c)), where a , b , c in R ~{0},exis...

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

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  19. ("lim")(xvec1)(1-x^2)/(s in2pix)i se q u a lto 1/(2pi) (b) -1/pi (c...

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

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