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Evaluate :underset(xrarr0)"lim"(sinx(1-c...

Evaluate :`underset(xrarr0)"lim"(sinx(1-cosx))/(x^(3))`

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The correct Answer is:
`(1)/(2)`
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CHHAYA PUBLICATION-LIMIT-IIIustrative Examples
  1. Evaluate :underset(xrarrpi)"lim"(sin3x)/(sin2x)

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  2. Evaluate :underset(xrarrpi)"lim"(1+cosx)/(x-pi)^(2)

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  3. Evaluate :underset(xrarr0)"lim"(sinx(1-cosx))/(x^(3))

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  4. Evaluate :underset(xrarr0)"lim"(x^(2)-tan2x)/(tanx)

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  5. Evaluate :underset(xrarr0)"lim"(cosec"x-cotx)/(x)

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  6. Evaluate :underset(xrarr0)"lim"(cos5x-cos7x)/(cosx-cos5x)

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  7. Evaluate :underset(xrarry)"lim"(sin^(2)x-sin^(2)y)/(x^(2)-y^(2))

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  8. Evaluate : underset(xrarr(pi)/(2))"lim"((pi)/(2)-x)tanx

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  9. Evaluate : underset(xrarr1)"lim"(1-x)"tan"(pix)/(2)

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  10. Evaluate : underset(xrarra)"lim"(xsina-asinx)/(x-a)

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  11. Evaluate : underset(hrarr0)"lim"(e^(5h)-1)/(3h)

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

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

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

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

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

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

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

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

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

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