   Chapter 2.5, Problem 34E

Chapter
Section
Textbook Problem

Locate the discontinuities of the function and illustrate by graphing. y = ln ( tan 2 x )

To determine

To locate: The discontinuities of the function y=ln(tan2x) and sketch the graph of the function y=ln(tan2x).

Explanation

Calculation:

The domain is the set of all input values of the function for which the function is real and defined.

Arbitrarily consider x=0, y=f(x) as undefined.

f(0)=ln(tan2(0))=ln(0)=

Substitute x=π2 in f(π2)=ln(tan2(π2)) does not exist.

Substitute x=π2 in f(π2)=ln(tan2(π2)) does not exist.

Substitute x=π in f(π)=ln(tan2(π)) is undefined.

Similarly, proceeding like this, f(x) is undefined at x=kπ2, where k is an integer.

The function f(x) is defined in except x=kπ2, where k

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