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Evaluate : underset(xrarr0)"lim"(root(3)...

Evaluate : `underset(xrarr0)"lim"(root(3)(1+x)-root(3)(1-x))/(x)`

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The correct Answer is:
`(2)/(3)`
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Evaluate : underset(xrarr0)"lim"(e^(x)-e^(-x))/(x)

Evaluate : underset(xrarr2)"lim"(2-sqrt(2+x))/(root(3)(2)-root(3)(4-x))

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CHHAYA PUBLICATION-LIMIT-IIIustrative Examples
  1. Prove that underset(hrarr0)"lim"(root3(x+h)-root3(x))/(h)=(1)/(3)x^(...

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  2. Prove that underset(xrarra)"lim"((x+5)^(5//2)-(a+5)^(5//2))/(x-a)=(...

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  3. Evaluate : underset(xrarr0)"lim"(root(3)(1+x)-root(3)(1-x))/(x)

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  4. Evaluate : underset(xrarr2)"lim"(2-sqrt(2+x))/(root(3)(2)-root(3)(4-x)...

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  5. Evaluate :underset(xrarr0)"lim"(tanx^(@))/(x)

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

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  7. underset(xrarr(pi)/(2))"lim"(cosx)/((pi)/(2)-x) =

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  8. Evaluate :underset(xrarrpi)"lim"(sin3x)/(sin2x)

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

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

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

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

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

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

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

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

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

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

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

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

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