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Chapter 6: Q. 6 (page 418)

True or False The graphs of

y=tanx,y=cotx,y=secx,andy=cscx

each have infinitely many vertical asymptotes.

Short Answer

Expert verified

It is true that the graphs of y=tanx,y=cotx,y=secx,andy=csxeach have infinitely many vertical asymptotes.

Step by step solution

01

Step 1. Given Information

The given functions are y=tanx,y=cotx,y=secx,andy=csx.

We have to state whether it is true or false that each function have infinitely many vertical asymptotes.

02

Step 2. Finding whether the statement is true or false

The function y=tanxhas asymptotes at卤n蟺2. Hence it has infinite asymptotes.

The function y=cotxhas asymptotes at 卤n蟺.Hence it has infinite asymptotes.

The function y=secxhas asymptotes at 卤n蟺2.Hence it has infinite asymptotes.

The function y=cscxhas asymptotes at 卤n蟺.Hence it has infinite asymptotes.

Thus, the statement is true.

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