How do you remove a removable discontinuity?

Answer 1

Please see the explanation section.

Function #f# has a removable discontinuity at #x=a# if #lim_(xrarra)f(x) = L# (for some real number #L#)
But #f(a) !=L#
We "remove" the discontinuity at #a#, by defining a new function as follows:
#g(x) = { (f(x),if,x != a),(L,if,x=a) :}#
For all #x# other than #a#, we see that #g(x) = f(x)#. and #lim_(xrarra)g(x) = L = g(a)#
So #g# is continuous at #a#.

(In more ordinary language, g is the same as f everywhere except at x = a, and g does not have a discontinuity at a.)

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Answer 2

To remove a removable discontinuity in a function, you need to redefine the function at the point of discontinuity. This can be done by evaluating the limit of the function as it approaches the point of discontinuity and assigning a new value to the function at that point. By doing so, you can create a continuous function without the removable discontinuity.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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