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Prove that lim(x rarr 0) ((1+x)^n-1)/(x...

Prove that `lim_(x rarr 0) ((1+x)^n-1)/(x)=n` .

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. Evaluate the following limit : lim(x rarr 1) (x^15-1)/ (x^10-1) .

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

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  3. Prove that lim(x rarr 0) ((1+x)^n-1)/(x)=n .

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  4. If lim(x rarr 2) (x^n-2^n)/(x-2)=80 and if n is a positive integer, fi...

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  5. Evaluate the following limit : lim(x rarr 3)(x^3-7x^2+15x -9)/(x^4-5...

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  6. Evaluate the following limit : lim(x to sqrt(2)) (x^(9) - 3x^(8) + x...

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

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

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

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  10. Evaluate the following limit : lim(x rarr 0) (sqrt(1+3x)-sqrt(1-3x))...

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

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

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  13. Evaluate the following limit : lim(x rarr 0) (sqrt(x+2)-sqrt2)/(x) .

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

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

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  16. Evaluate the following limit : lim(h rarr 0) 1/h[1/(x+h)-1/(x)] .

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

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  18. Find all possible values of a, if : lim(x rarr a) (x^9-a^9)/(x-a)= l...

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  19. Find all possible values of a, if : lim(x rarr a) (x^3-a^3)/(x-a)= l...

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  20. Evaluate underset(zto1)(lim)(z^(1//3)-1)/(z^(1//6)-1)

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