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

Evaluate the following limit :
`lim_(x rarr 0) (sqrt(1+3x)-sqrt(1-3x))/(x)` .

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

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Prove that : lim(x rarr 0) (|x|)/(x) does not exist.

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  15. Prove that : lim(x rarr 0)(x)/(|x|) does not exist.

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  16. Prove that : lim(x rarr 0^+)(x)/(|x|)=1 .

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  17. Prove that : lim(x rarr 0^-)(x)/(|x|)= -1 .

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

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  19. Find lim(x rarr 0) f(x), and lim(x rarr 1) f(x), where : f(x)= {(2x+3...

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  20. Find lim(x rarr 0) f(x), where f (x) =|x|-5.

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