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

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

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. Evaluate the following limit : lim(x rarr 0)((e^x-e^(-x))/(sinx)) .

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

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

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

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

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

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

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

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

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  10. If g(t) = 1- 4t^2, find g’(1).

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

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  12. If f(x) =x^3+7x^2+8x-9, find f'(4).

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  13. Find the derivative of f, defined by f (x) =mx +c at x = 0.

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  14. Find f’(2) and f’(5), where f(x) =x^2+7x+4 .

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  15. If f(x) =x^2-19x + 18, then find f’(2), f’ (1) and f’ (10), using limi...

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  16. Show that the derivative of the function f, given by : f (x) =2x^3-9x...

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  17. For the function f, f(x)=x^2-4x+7 , show that f '(5)= 2f'(7/2) .

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  18. For the function f, f(x)=x^2-6x + 8, prove that f’(5)-3 f'(2)= f’(8).

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  19. Given f(x) = 2x^3, find f'(x) by delta method.

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  20. If f : R rarr R and g : R rarr R be two mapping such that f(x) = sin x...

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