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("lim")(xvec2)(((x^3-4x)/(x^3-8))^(-1)-(...

`("lim")_(xvec2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1))i se q u a lto` a)`1/2` (b) 2 (c) 1 (d) none of these

A

1

B

`1//2`

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xto2)lim[((x(x-2)(x+2))/((x-2)(x^(2)+2x+4)))^(-1)-((sqrt(x)"("sqrt(x)+sqrt(2")"))/("("sqrt(x)-sqrt(2")")"("sqrt(x)+sqrt(2")"))-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1)]`
`=underset(xto2)lim[(x^(2)+2x+4 )/(x(x+2))-((sqrt(x)-sqrt(2))/(sqrt(x)-sqrt(2)))^(-1)]`
`=underset(xto2)lim[(x^(2)+2x+4)/(x(x+2))-1]=12/8-1=1/2`
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CENGAGE-LIMITS-Exercise (Single)
  1. The value of ("lim")(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a)1/(...

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  2. The value of ("lim")(xvec2)(2^x+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))i s ...

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  3. ("lim")(xvec2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(...

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  4. about to only mathematics

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  5. ("lim")(xvec1)((1-x)(1-x^2)(1-x^(2n)))/({(1-x)(1-x^2)(1-x^n)}^2),n in ...

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  6. The value of lim(xto(1)/(sqrt(2))) (x-cos(sin^(-1)x))/(1-tan(sin^(-1)x...

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

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

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

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

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  12. about to only mathematics

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

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

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

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

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

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

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

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