anonymous
  • anonymous
give an example
Calculus1
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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
experimentX
  • experimentX
try this \[ \lim_{x \to 0}{\sin^2x x \over x^2}\] expand sin^2 x as 1 + cos^2x
anonymous
  • anonymous
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 \[ \lim_{x \rightarrow \infty}f(x)+g(x)=-1\]

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experimentX
  • experimentX
try something like of this form where you can take LCM and use L'Hopital's rule \[ \infty - \infty \]
experimentX
  • experimentX
@REMAINDER 's example is also good example.
experimentX
  • experimentX
Woops!! \[ \lim_{x \to 0}{\sin^2x \over x^2} = \lim_{x \to 0}{1 \over x^2}+\lim_{x \to 0}{\cos^2 x \over x^2}\]
anonymous
  • anonymous
???
experimentX
  • experimentX
both 1/x^2 and cos^2x/x^2 does not exist but the sum exists
anonymous
  • anonymous
how to know exist or not
experimentX
  • experimentX
try finding them individually ...
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=lim+x-%3E0+cos^2x%2Fx^2

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