Determine the end behavior of the following transcendental functions by

James Dale

James Dale

Answered question

2022-01-13

Determine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist.
f(x)=sinx

Answer & Explanation

redhotdevil13l3

redhotdevil13l3

Beginner2022-01-14Added 30 answers

Step 1
Substitute for x
limx=limxsin()
Simplify
=Undefined
Substitute for x
limxf(x)=limxsin()
Simplify
=Undefined
Step 2
Sine is defined on entire domain so we have no vertical asymptotes.
For slant asymptotes, we check the lines.
Using formula limx±f(x)x=k where k represents slope of our line (slant asymptote).
Table limit
limxf(x)x=limxsin(x)x
Simplify
=0
Therefore, there is no slant asymptote.
image

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