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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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CENGAGE ENGLISH-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. ("lim")(xvecoo)"{"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 lim(x->2^-) (ae^(1/|x+2|)-1)/(2-e^(1/(|x+2|)))= lim(x->2^+)sin ((x^...

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

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  6. lim(x->o)[(x^4sin(1/x)+x^2)/(1+|x|^3)]=

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  7. Evaluate the limit: ("lim")(xvecoo)((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 to 0)(x^4((cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)))"is equals t...

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

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  12. ("lim")(xrarroo)(1/e-x/(1+x))^x is equal to (a) e/(1-e) (b) 0...

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  13. Evaluate: ("lim")(xrarr0)(cosx)^(cotx)

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

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  15. Evaluate ("lim")(xvec0)((sinx)/x)^(((sinx)/(x-sinx)))

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

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  17. Evaluate: ("lim")(xvec0) ((1+x)^(1/x)-e+1/2e x)/(x^2)

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  18. ("lim")(xvec0)(x^asin^b x)/(sin(x^c)), where a , b , c in R ~{0},exis...

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  19. ("lim")(xvec0)(5sinx-7sin2x+3sin3x)/(x^2sinx)

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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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