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aiskarl

  • 3 years ago

give an example

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  1. aiskarl
    • 3 years ago
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    give an example to show that \[\lim_{x \rightarrow a} f(x)\] and \[\lim_{x \rightarrow a} g(x)\] doesnot exist but \[\lim_{x \rightarrow a} (f(x)+g(x))\] exist

  2. experimentX
    • 3 years ago
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    try this \[ \lim_{x \to 0}{\sin^2x x \over x^2}\] expand sin^2 x as 1 + cos^2x

  3. REMAINDER
    • 3 years ago
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    let f(x)=x and g(x)=-(x+1) and a=infinity then \[\lim_{x \rightarrow \infty } f(x)=\infty \] and \[ \lim_{x \rightarrow \infty } g(x)=-\infty\] but \[ \lim_{x \rightarrow \infty}f(x)+g(x)=-1\]

  4. experimentX
    • 3 years ago
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    try something like of this form where you can take LCM and use L'Hopital's rule \[ \infty - \infty \]

  5. experimentX
    • 3 years ago
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    @REMAINDER 's example is also good example.

  6. experimentX
    • 3 years ago
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    Woops!! \[ \lim_{x \to 0}{\sin^2x \over x^2} = \lim_{x \to 0}{1 \over x^2}+\lim_{x \to 0}{\cos^2 x \over x^2}\]

  7. aiskarl
    • 3 years ago
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    ???

  8. experimentX
    • 3 years ago
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    both 1/x^2 and cos^2x/x^2 does not exist but the sum exists

  9. aiskarl
    • 3 years ago
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    how to know exist or not

  10. experimentX
    • 3 years ago
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    try finding them individually ...

  11. experimentX
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=lim+x-%3E0+cos^2x%2Fx^2

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