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Prove that : lim(x to 0^(+))x/abs(x)=1...

Prove that :
`lim_(x to 0^(+))x/abs(x)=1`

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE 13 (a)
  1. Evaluate the following limit: (lim)(x->0)(sqrt(1+x)-sqrt(1-x))/(2x)

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

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

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

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

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

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

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

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

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

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

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

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  14. Prove that : lim(x to 0)abs(x)/x does not exist

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  15. Prove that : lim(x to 0)x/abs(x) does not exist

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  16. Prove that : lim(x to 0^(+))x/abs(x)=1

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  17. Prove that : lim(x to 0^(-))x/abs(x)=-1.

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  18. If the function f(x) satisfies lim(x to 1) (f(x)-2)/(x^(2)-1)=pi, then...

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  19. Find lim(x to 0)f(x), where f(x)=abs(x)-5.

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  20. Evaluate lim(x to 0)f(x), where : " "f(x)={{:(x/abs(x)",", x ne 0)...

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