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Prove that underset(xrarr0)"lim"((1+x)^(...

Prove that `underset(xrarr0)"lim"((1+x)^(n) - 1)/(x) = n`.

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE 13 (a)
  1. Evaluate the following limits : lim(x to 1)(x^(15)-1)/(x^(10)-1)

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

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  3. Prove that underset(xrarr0)"lim"((1+x)^(n) - 1)/(x) = n.

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  4. If ("lim")(xvec2)(x^n-2^n)/(x-2)=80a m dm in N ,t h e nfin dt h ev a ...

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  5. lim(x->3) {x^3-7x^2+15x-9}/{x^4-5x^3+27x-27} is equal to:

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  6. Evaluate: (lim)(x->sqrt(2))(x^9-3x^8+x^6-9x^4-4x^2-16 x+84)/(x^5-3x^4-...

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

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  8. Evaluate the following limit: (lim)(x->0)(sqrt(1+x)-sqrt(1-x))/(2x)

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  9. Evaluate the following limits: lim(xto0)((sqrt(2-x)-sqrt(2+x))/(x))

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  10. Evaluate the following limits : lim(x to 0)(sqrt(1+3x)-sqrt(1-3x))/(...

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

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

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  13. Evaluate the following limits : lim(x to 0)(sqrt(x+2)-sqrt(2))/x

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

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

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

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  17. lim(x->2)[1/(x-2)-(2(2x-3))/(x^3-3x^2+2x)]

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  18. Find all possible values of 'a', if : lim(x to a)(x^(9)-a^(9))/(x-a)...

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  19. If (lim)(x->a)(x^3-a^3)/(x-a)=(lim)(x->1)(x^4-1)/(x-1) , find all poss...

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  20. underset(z rarr1)"lim"(2^(1//3)-1)/(z^(1//6)-1)

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