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How do you find the vertical, horizontal and slant asymptotes of: # g(theta) = tan(theta)/(theta)#?

Answer 1

Serenity Jones

See below.

Vertical asymptotes occur at values that make the function undefined. No interval has been specified so I will use:

#-2pi<=theta<=2pi#

#tan(theta)# is undefiled for, #-(3pi)/2 -pi , pi/2 , (3pi)/2#

The function is also undefined for #theta = 0# ( Division by 0 )

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Answer 2

Serenity Johnson

To find the vertical asymptotes, set the denominator equal to zero and solve for theta. For horizontal asymptotes, look at the behavior of the function as theta approaches positive or negative infinity. There are no slant asymptotes for this function.

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Answer from HIX Tutor

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.