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The value of lim(xto2) (((x^(3)-4x)/(x^(...

The value of `lim_(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1))" is "`

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)
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  2. The value of lim(xto2) (2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))" is "

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  3. The value of lim(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2...

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  4. If lim(xto-2^(-)) (ae^(1//|x+2|)-1)/(2-e^(1//|x+2|))=lim(xto-2^(+)) si...

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  5. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

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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. Among (i) lim(xtooo) sec^(-1)((x)/(sinx))" and "(ii) lim(xtooo) sec^(-...

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

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  9. lim(ntooo) (n(2n+1)^(2))/((n+2)(n^(2)+3n-1))" is equal to "

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  10. lim(xtooo) ((2x+1)^(40)(4x+1)^(5))/((2x+3)^(45)) is equal to

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

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  12. lim(xtooo) (2+2x+sin2x)/((2x+sin2x)e^(sinx)) is equal to

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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(xtooo) (2sqrt(x)+3root(3)(x)+4root(4)(x)+...+nroot(n)(x))/(sqrt((2...

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  15. If lim(ntooo) (n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then the ran...

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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(ntooo) (1)/(((3)/(pi)tan^(-1)2x)^(2n)+5). 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(ntooo) [(2n)/(2n^(2)-1)"cos"(n+1)/(2n+1)-(n)/(1-2n).(...

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

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