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Bring one specific function for which the limit fails to exist.
Explain the reason why you think that the limit DNE. (specify where it DNE).
lim as x approaches 0 at sin(1/x) is a limit that does not exist because, as x is reaching to 0, it begins to oscillate more and more. -Tanvir
Great Tranvir! I have to highlight that I am looking for examples different from what we have done in class.
Thanks!
One example where the limit does not exist is the limit as x approaches to zero when f(x) is equal to radical (x) since this function is only defined for x values from the right, we can’t have values less than zero (from the left) because it will be irrational.
-Diego Guaman
Great Diego! I just want to clarify something. The limit from the left does not exist in the real set of numbers, because it would be square root of negative number (imaginary root). Square root of 2 for example is irrational, but it is real number.
A problem where the limit fails to exist would be lim F(X) x->3. The graph will only let you do a one-sided limits, the value F(X) is still approaching depends on the direction of X. The limit does not exist.
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