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

`lim_(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^(2)),`n in N`, `equals`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If lim xto0(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then (a)...

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  2. If lim(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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

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  4. The value of lim(x->0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] repre...

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  5. The value of lim(x->1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(sin^(-...

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  6. The value of underset(xtooo)lim((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((...

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  7. Let lim(xto0) ([x]^(2))/(x^(2))=m, where [.] denotes greatest integer....

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  8. underset(xto1)lim(xsin(x-[x]))/(x-1), where [.] denotes the greatest i...

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  9. underset(xto0)lim[(sin(sgn(x)))/((sgn(x)))], where [.] denotes the gre...

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

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  11. If f(x)=(cosx)/((1-sinx)^(1/3)) then (a) ("lim")(xrarrpi/2)f(x)=-oo (b...

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  12. lim(x->-oo)(x^2*tan(1/x))/(sqrt(8x^2+7x+1)) is

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  13. T1 is an isosceles triangle in circle C. Let T2 be another ísoscele...

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

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  15. lim(xtooo) [((e)/(1-e))((1)/(e)-(x)/(1+x))]^(x) is :

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  16. ("lim")(x -> 0)((1+tanx)/(1+sinx))^(cos e cx) is equal to (a)e ...

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  17. lim(x->oo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 ...

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  18. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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  19. "Find"(dy)/(dx)"if "y=tan^(-1)((sqrt(1+x^2)-1)/x), where x!=0

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  20. (c)answer any three questions: 1. if y=sin ^(-1) ((2x)/(1+x^2)) , find...

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