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Evaluate the following limits: lim(xto...

Evaluate the following limits:
`lim_(xto0)(sqrt(cosx)-root3cosx)/(sin^(2)x)`

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The correct Answer is:
`-(1)/(12)`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-CALCULUS
  1. Evaluate the following limits: lim(ntooo)[(n)/(n^(2))+(n+1)/(n^(2))+...

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  2. Evaluate the following limits: lim(xto3)(3-sqrt(6+x))/(3sqrt3-sqrt(6...

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  3. Evaluate the following limits: lim(xto0)(sqrt(cosx)-root3cosx)/(sin^...

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  4. Evaluate the following limits: lim(xto0)[coec^(3)xcotx-2cot^(3)xcose...

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  5. Evaluate the following limits: lim(xto(pi)/(2))(xtanx-(pi)/(2)secx)

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  6. Show that lim(xto1)(sqrt(1-cos(x-1)))/(x-1) does not exist.

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  7. Evaluate: lim(xto2)(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))

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  8. Evaluate: lim(xto(pi)/(2))((2xsecx)/(pi)-tanx)

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  9. Evaluate: lim(xto0)(cosx)^(cot^(2)x)

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  10. Evaluate: lim(xto(1)/(2))(cos^(2)pix)/(e^(2x)-2ex)

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  11. Evaluate: lim(xto(pi)/(3))(tan^3x-3tanx)/(cos(x+(pi)/(6)))

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  12. Evaluate: lim(xtoa)(ae^(x)-xe^(a))/(x-a)

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  13. Evaluate: lim(xto0)(e^(x)-log(e+ex))/(x)

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  14. Evaluate: lim(xto(pi)/(2))(1+cosx)^(3secx)

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  15. Evaluate: lim(xto(1)/(2))(sin((pix)/(2))-cos((pix)/(2)))/((1)/(2)-x)

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  16. Evaluate: lim(xto0)((x-1+cosx)/(x))^(1//x)

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  17. Evaluate: lim(xto2)(sqrt(1+sqrt(2+x))-sqrt3)/(x-2)

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  18. Evaluate: lim(xto0)(sinx+cosx)^(1//x)

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  19. Evaluate: lim(xto0)[tan(x+(pi)/(4))]^(1//x)

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  20. Evaluate: lim(xto0)(1)/(x^(3))[sin(3x+a)-3sin(2x+a)+3sin(x+a)-sina]

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