Learn how to find horizontal asymptotes of various functions using limits in this comprehensive calculus tutorial. Explore seven detailed examples covering rational, trigonometric, radical, and exponential functions. Discover techniques for determining asymptotes as x approaches both positive and negative infinity, and understand how functions can have zero, one, or two horizontal asymptotes. Master this essential calculus concept through step-by-step explanations and diverse problem-solving approaches.

Syllabus

Intro
Horizontal Asymptotes of x^2-1/x^2+1
Horizontal Asymptotes of tan^-1x
Horizontal Asymptotes of 1/x
Horizontal Asymptotes of 3x^2-x-2/5x^2+4x+1
Horizontal Asymptotes of Rational Functions
Horizontal Asymptotes of 3x-2/sqrt2x^2+1
Horizontal Asymptotes of sqrtx^2+1-x
Horizontal Asymptotes of e^x
Conclusion