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Evaluate : underset(xrarr1)"lim"(e^(logx...

Evaluate : `underset(xrarr1)"lim"(e^(logx)-1)/(e^(x-1)-1)`

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Evaluate : underset(xrarr0)"lim"(sin^(-1)x)/(2x)

underset(xrarr0)"lim"(a^(2x)-1)/(x) =

Evaluate : underset(xrarr1)"lim"sin(2x^(2)-x-1) .

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underset(xrarr1)"lim"(x-1)/(sqrt(x)-1)= ?

CHHAYA PUBLICATION-LIMIT-IIIustrative Examples
  1. Evaluate : underset(hrarr0)"lim"(e^(5h)-1)/(3h)

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  2. Evaluate : underset(xrarr0)"lim"(e^(px)-e^(-qx))/(x)

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  3. Evaluate : underset(xrarr1)"lim"(e^(logx)-1)/(e^(x-1)-1)

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  4. Evaluate : underset(xrarr2)"lim"(e^(x)-e^(2))/(x-2)

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  5. Prove that, underset(x rarr 0)(lim)(5^(x)-4^(x))/(x)=log(e)((5)/(4))

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  6. Evaluate: underset(x rarr 0)(lim)log(1+alphax)/(e^(2x)-1)

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  7. Evaluate : underset(xrarr0)"lim"(e^(ax)-1)/(sinbx)

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  8. Evaluate : underset(xrarr0)"lim"(sinx)/(log(e)(1+x)^(1//4))

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  9. Evaluate : underset(xrarr0)"lim"((e^(x)-1)log(1+x))/(sin^(2)x)

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  10. Evaluate : underset(xrarr0)"lim"(3^(x)-1)/((4+x)^(1//2)-2)

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  11. Evaluate :underset(nrarroo)"lim"(n^(4)-n^(2)+6n+1)/(2n^(4)-5n+4)

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  12. Evaluate :underset(xrarroo)"lim"(sqrt(x^(2)+ax)-x).

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  13. Prove that underset(nrarroo)"lim"(1^(3)+2^(3)+3^(3)+...+n^(3))/(n^(4))...

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  14. Show that underset(xrarr0)"lim"(xtan2x-2xtanx)/((1-cos2x)^(2))=(1)/(2)

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  15. Examine the existence of the following limits : underset(xrarr2)"li...

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  16. Examine the existence of the following limits : underset(xrarr3)"lim...

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  17. Prove that underset(xrarr0)"lim"(3x+|x|)/(7x-5|x|)does not exist .

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  18. Does underset(xrarra)"lim"f(x)=underset(xrarra)"lim"phi(x) "always imp...

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  19. Examine the existence of the following of limits : underset(xrarr...

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  20. Examine the existence of the following of limits : underset(xrarr0)"l...

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