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The reciprocal of the value of: ("lim")(...

The reciprocal of the value of: `("lim")_(ntooo)(1-1/(2^2))(1-1/(3^2))(1-1/(4^2))(1-1/(n^2))i s `

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Verified by Experts

The correct Answer is:
`(2)`
We have
`L=underset(ntooo)limprod_(n=2)^(n)(n^(2)-1)/(n^(2))`
`=underset(ntooo)limprod_(n=2)^(n)(n-1)/(n).prod_(n=2)^(n)(n+1)/(n)`
`=underset(ntooo)lim((1)/(2).(2)/(3).(3)/(4)...(n-1)/(n))((3)/(2).(4)/(3).(5)/(4)...(n+1)/(n))`
`=underset(ntooo)lim(1)/(n).(n+1)/(2)=(1)/(2)`
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CENGAGE-LIMITS-Exercise (Numerical)
  1. The reciprocal of the value of: ("lim")(ntooo)(1-1/(2^2))(1-1/(3^2))(1...

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  2. lim(xrarrinfty)f(x),where (2x-3)/xltf(x)lt(2x^2+5x)/x^2,is

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  3. If f(x)={x-1,xgeq1 2x^2-2,x<1,g(x)={x+1,x >0-x^2+1, xlt=0,and h(x)=|...

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  4. If ("lim")(xvecoo)f(x) exists and is finite and nonzero and if ("lim"...

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  5. If L-("lim")(xvec2)((10-x)^(1/3)-2)/(x-2),t h e nt h ev a l u eof|1(4L...

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  6. If lim(xto0) (p sin2x+(1-cos2x))/(x+tanx)=1, then the value of p is.

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  7. The value of lim(xtooo) ((100)/(1-x^(100))-(50)/(1-x^(50))) is .

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  8. If L-("lim")(xvec2)((10-x)^(1/3)-2)/(x-2),t h e nt h ev a l u eof|1(4L...

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  9. The value of underset(xtooo)lim((100)/(1-x^(100))-(50)/(1-x^(50))) is ...

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  10. The value of ("lim")(xvecoo)[3sqrt((n+1)^2) -3sqrt((n-1)^2 ))] is

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  11. If L=("lim")(nvecoo)(2x3^2x2^3x3^4..... x2^(n-1)x3^n)^(1/((n^(2+1))) ,...

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  12. The value of ("lim")(xvecoo)((log)e((log)e x)/(e^(sqrt(x)))) is

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  13. about to only mathematics

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  14. The value of lim(x to oo ) (x-x^(2)log(e)(1+(1)/(x))) is .

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  15. Let S(n)=1+2+3+...+n " and " P(n)=(S(2))/(S(2)-1).(S(3))/(S(3)-1).(S(4...

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  16. If ("lim")(xvec1)(asin(x-1)+bcos(x-1)+4)/(x^2-1)=-2,t h e n|a+b| is

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  17. Let ("lim")(x to1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(...

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  18. Evaluate underset(xto1)lim((2)/(1-x^(2))-(1)/(1-x)).

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  19. If: ("lim")(xvec1)(1+a x+b x^2)^(c/((x-1)))=e^3, then the value ofb c ...

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  20. Let f ''(x) be continuous at x=0 If ("lim")(xvec0)(2f(x)-3a(f(2x)+bf(...

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