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If f(n)=underset(xto0)lim{(1+"sin"(x)/(2...

If `f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"sin"(x)/(2^(n)))}^((1)/(x))` then find `underset(ntooo)limf(n).`

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If f(n)=lim_(xto0) {(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"sin"(x)/(2^(n)))}^((1)/(x)) then find lim_(ntooo) f(n).

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate: ("lim")(xrarr0)((a^x+b^x+c^x)/3)^(2/x);(a , b , c >0)

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  2. underset(xtooo)lim{(x+5)tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to

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  3. If f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"s...

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

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  5. The population of a country increases by 2% every year. If it increase...

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  6. Evaluate lim(xto-oo)[(x^(4)sin((1)/(x))+x^(2))/((1+|x|^(3)))].

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  7. Evaluate the limit: lim(x->oo)((x+2)/(x+1))^(x+3)

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  8. ABC is an isosceles triangle inscribed in a circle of radius rdot If A...

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  9. Evaluate: lim(x->pi/2)(cosx)^(cosx)

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  10. lim(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (...

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  11. Evaluate: lim(x->0)(1+x)^(cos e cx )

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  12. lim(x->oo)(1/e-x/(1+x))^x is equal to (a) e/(1-e) (b) 0 (c) e/(e^...

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  13. Evaluate: lim(x->0)(cosx)^(cotx)

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  14. lim(x->1)(1-x^2)/(sin2pix) is equal to (a)1/(2pi) (b) -1/pi (...

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  15. Evaluate ("lim")(xto0)((sinx)/x)^(((sinx)/(x-sinx)))

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  16. lim(xtooo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 ...

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  17. Evaluate lim(xto0) ((1+x)^(1//x)-e+(1)/(2)ex)/(x^(2)).

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  18. If lim(x→0) ​ (x^asin^b x)/(sin(x^c)), where a , b , c in ...

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  19. Evaluate underset(xto0)lim(5sinx-7sin2x+3sin3x)/(x^(2)sinx).

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  20. ("lim")(x->oo){(x^3+1)/(x^2+1)-(a x+b)}=2,t h e n (a)a=1,b=1 (...

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