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Understanding The Asymptote

  1. It will never cross the curve.


1031. It is a line of the form y = k.

  1. It is a slanting line and hence its equation is of the form y = mx + b.


921.      True or False: Polynomial functions, sine, and cosine functions have no horizontal or vertical asymptotes.

True or False: Trigonometric functions csc, sec, tan, and cot have vertical asymptotes but no horizontal asymptotes

It may cross the curve sometimes

  1. It is a line of the form x = k.


True or False: If a function has a horizontal asymptote, then it cannot have a slant asymptote and  vice versa.

1035. It is obtained by taking the limit as y→∞ or y→ -∞.

1034. It is obtained by taking the limit as x→∞ or x→ -∞.