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

`lim_(x to oo )((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2))` is equal to

A

`2`

B

`-1`

C

`0`

D

`2/9`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xtooo)lim((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2))=underset(xtooo)lim(x^(3)(3x+2)-x^(2)(3x^(2)-4))/((3x^(2)-4)(3x+2))`
`=underset(xtooo)lim(2x^(3)+4x^(2))/(9x^(3)+6x^(2)-12x-8)`
`=underset(xtooo)lim(2+(4)/(x))/(9+(6)/(x)-(12)/(x^(2))-(8)/(x^(3)))`
`=2//9`
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CENGAGE-LIMITS-Exercise (Single)
  1. The value of lim(xto(1)/(sqrt(2))) (x-cos(sin^(-1)x))/(1-tan(sin^(-1)x...

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  2. evaluate (i) underset(xtooo)limsec^(-1)((x)/(sinx))" and "(ii) underse...

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

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

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

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  7. about to only mathematics

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

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

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

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

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

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

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

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

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

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

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

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

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