# How do you locate the discontinuities of the function #y = ln(tan(x)2)#?

The first thing to look at is where the ln function has discontinuities. The natural log function looks at the value in parentheses and evaluates the power to which e, Euler's number, must be raised to be equal to the value in the parentheses. For example:

As a result, this has discontinuities if

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To locate the discontinuities of the function y = ln(tan(x)^2), we need to consider the values of x that make the function undefined.

The function ln(tan(x)^2) is undefined when the argument of the natural logarithm, tan(x)^2, is less than or equal to zero.

To find the values of x that satisfy this condition, we can set tan(x)^2 ≤ 0 and solve for x.

Since the square of any real number cannot be negative, there are no real values of x that make tan(x)^2 ≤ 0.

Therefore, the function y = ln(tan(x)^2) is continuous for all real values of x.

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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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