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

`lim_(x rarr 0)ln(1+3x)/(3^x-1)`

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The correct Answer is:
`3/(log_(e)3)`
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lim_(x rarr0)(log(1+x))/(x)=1

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE 13 (c)
  1. Evaluate the following limits : lim(x to 1)(logx)/(x-1)

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Evaluate the following limits : lim(x to pi/2)(e^(sinx)-1)/sinx

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  15. Evaluate the following limits : lim(x to pi/2)(e^(cosx)-1)/cosx

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  16. Evaluate the following limits : lim(x to 0)(e^(sin2x)-e^(sinx))/x

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

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  18. Evaluate the following limits : lim(x to 0)(x(e^(2+x)-e^(2)))/(1-cos...

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  19. Evaluate the following limits : lim(x to 0)(x(2^(x)-1))/(1-cosx).

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  20. Evaluate the following limits : lim(x to pi/2)(2^(-cosx)-1)/(x(x-pi...

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