# What does it mean when it says: "non-removable discontinuity at x=4"?

See the explanation.

Here is the definition I am familiar with.

In the most familiar functions:

Rational and trigonometric functions have non-removable discontinuities at their vertical asymptotes. (Holes are removable.)

Piecewise-defined functions can have jump discontinuities, which are non-removable. (Holes are removable.)

The Greatest integer function (a.k.a. the Floor function) has a non-removable discontinuity at every integer.

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A non-removable discontinuity at x=4 means that the function has a break or hole in its graph at x=4. The function is undefined at this point, and there is no way to remove or fill in the gap to make the function continuous at x=4.

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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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- What is the limit of #xsinx# as x approaches infinity?
- What are the asymptotes of #f(x)=-x/((2x-3)(4x-8)) #?
- Find the limit for the given function? #lim_(t->0) text( ) ((text(sin)(8 t))^2)/t^2#
- How do you find discontinuity algebraically?

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