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find All disuntiniteas
Log x + 4x³
——————
X

1 Answer

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I believe the expression you provided is:

(log(x) + 4x^3) / x

To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.

There are two types of discontinuities to look for:

Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.

Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.

To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.

So we solve the equation:

x = 0

This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.

Therefore, the only discontinuity of the expression is at x = 0.

Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.

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