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Evaluate the following limit : lim(x r...

Evaluate the following limit :
`lim_(x rarr 0)(e^(sinx)-1)/x` .

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. Evaluate the following limit : lim(x rarr 0)[1/x-(log(1+x))/x^2] .

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  2. Evaluate the following limit : lim(x rarr 2)(3^x+3^(3-x) - 12)/(3^(3...

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  3. Evaluate the following limit : lim(x rarr 0)(e^(sinx)-1)/x .

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  4. Evaluate the following limit : lim(x rarr 0)(e^(tan x)-1)/x .

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  5. Evaluate the following limit : lim(x rarr 0)(e^(sinx)-1)/(sinx) .

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  6. Evaluate the following limit : lim(x rarr 0)(e^(tan x)-1)/(tan x) .

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  7. Evaluate the following limit : lim(x rarr pi/2)(e^(sinx)-1)/(sinx) .

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  8. Evaluate the following limit : lim(x rarr pi/2)(e^(cos x)-1)/(cos x)...

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  9. Evaluate the following limit : lim(x rarr 0)(e^(sin 2x)-e^(sinx)) /(...

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  10. Evaluate the following limit : lim(x rarr 0)((e^x-e^(-x))/(sinx)) .

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  11. Evaluate the following limit : lim(x rarr 0)(x(e^(2+x)-e^2))/(1-cosx...

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  12. Evaluate the following limit : lim(x rarr 0)(x(2^x-1))/(1-cosx) .

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  13. Evaluate the following limit : lim(x rarr pi/2)(2^(-cosx)-1)/(x(x- p...

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  14. Evaluate the following limit : lim(x rarr 0)(sqrt(1+x)-1)/(log(1+ x)...

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  15. Evaluate the following limit : lim(x rarr 0)(2^x-1)/(sqrt(1+x)-1) .

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  16. Evaluate the following limit : lim(x rarr 0)(5^x-1)/(sqrt(4+x)-2) .

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  17. Find the derivative at x = 2 of the function f(x) = 3x.

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  18. Find the derivative of f(x) = sin x at x = 0.

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  19. If g(t) = 1- 4t^2, find g’(1).

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  20. If f(x) =x^2+2x+7, find f'(3).

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