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Evaluate the following limits: lim(xt...

Evaluate the following limits:
`lim_(xto0)((a^(x)-a^(-x))/(x))`

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The correct Answer is:
`2log_(e)a`
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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE 13 (c)
  1. Evaluate the limits, if exist (lim)(x->3)(e^x-e^3)/(x-3)

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  2. Evaluate the following limits: lim(xto0)((a^(x)-b^(x))/(x))

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  3. Evaluate the following limits: lim(xto0)((a^(x)-a^(-x))/(x))

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  4. Evaluate the following limits : lim(x to 0)(e^(x)-e^(-x))

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  5. Evaluate the following limits : lim(x to 0)(e^(x)-e^(-x))/x

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  6. Evaluate the following limits : lim(x to 1)(e^(-x)-e^(-1))/(x-1)

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  7. Evaluate the following limits : lim(x to 1)(e^(x)-e^(-x))/(e^(x)+e^(...

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  8. Evaluate the following limits : lim(x to 0)(e^(x)-e^(-x))/sinx.

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  9. Evaluate the following limits : lim(x to 0)(e^(bx)-e^(ax))/x, where ...

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  10. Evaluate the following limits : lim(x to 1)(logx)/(x-1)

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  11. Evaluate the following limits : lim(x to 1)(x-1)/(logx).

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  12. lim(x rarr 0)ln(1+3x)/(3^x-1)

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  13. Evaluate the following limits : lim(x to 0)(log(1+x))/(e^(x)-1).

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  14. Evaluate the following limits : lim(x to 3)(logx-log3)/(x-3)

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  15. Evaluate the following limits : lim(x to 0)(log(3+x)-log(3-x))/x.

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  16. Evaluate the following limits : lim(x to infty)(sin(a/2^(x)))/sin(b/2^...

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  17. Evaluate the following limits : lim(x to 0)[1/x-(log(1+x))/x^(2)]

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  18. Evaluate the following limits : lim(x to 2)(3^(x)+3^(3-x)-12)/(3^(3-...

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  19. Evaluate the following limits : lim(x to 0)(e^(sinx)-1)/x

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  20. Evaluate the following limits: lim(xto0)((e^(tanx)-1))/(x)

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