Limits at Infinity with Horizontal and Vertical Asymptotes

Which of the following actions are appropriate for finding a limit at infinity? Look for multiple answers.

• If the function is polynomial, look at rules for end behavior.

• If the function has a HA, that will determine the limit at infinity.

• If the function has a slant asymptote, look at the end behavior of that line (the slant asymptote)

• Look at the function graphically to determine end behavior.

Find the limit. Hint: Where is the horizontal asymptote?

• ³/₇

• 0

• ∞

• -∞

Find the limit. Hint: Where is the horizontal asymptote?

• ^-2/₉

• 0

• ∞

• -∞

• 0

• DNE

• 1/2

• 2

• 2

• 2/3

• 2

• 3

• x

• e

Which statement is true about slant asymptotes?

• Slant asymptotes can be a vertical or horizontal line graphically.

• Slant asymptotes are oblique (not purely vertical or horizontal) lines graphically.

• Slant asymptotes occur when the degree of the denominator is greater.

• Slant asymptotes occur when the degree of the numerator and denominator are equal.