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Prove that : lim(x rarr 0) (|x|)/(x) do...

Prove that : `lim_(x rarr 0) (|x|)/(x)` does not exist.

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. Find all possible values of a, if : lim(x rarr a) (x^3-a^3)/(x-a)= l...

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

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

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

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

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

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

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

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

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  10. Find underset(xrarr0)lim f(x), where f(x)={(|x|/x, xne0),(0, x=0):}

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  11. Find underset(xrarr0)lim f(x), where f(x)={(|x|/x, xne0),(0, x=0):}

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  12. Let f(x)= {(|x|+1,",", x<0),(0,",", x=0),(|x|-1,",", x>0.):} For what...

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  13. If f(x)= {:(mx^(2)+n, x lt 0),(nx +m,0le x le 1),(nx^(3) +m, x gt 1):}...

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  14. Evaluate the following : lim(x rarr 0)(cos x)/(pi-x) .

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  15. Evaluate the following : lim(theta rarr 0)(1-cos theta)/(2 theta^2)...

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  16. Evaluate the following : lim(x rarr 0)(1-cos 4x)/(x^2) .

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  17. Evaluate the following : lim(x rarr 0)(1-cos 4x)/(x^2) .

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

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  19. Evaluate the following : lim(theta rarr 0)(1-cos 4 theta)/(1-cos 6 ...

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  20. Evaluate the following : lim(x rarr 0)(cos 2x-1)/(cos x-1) .

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