Infinite Limits 1.5. An infinite limit is a limit in which f(x) increases or decreases without bound as x approaches c. Be careful…the limit does NOT.

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Presentation transcript:

Infinite Limits 1.5

An infinite limit is a limit in which f(x) increases or decreases without bound as x approaches c. Be careful…the limit does NOT exist.

Ex) Find the limits from the graph.

Ex) Find the limit using a table. X f(x) ?

Ex) Find the limit analytically. **hint: pick a number close to 1 from the left

Ex) Find the limit analytically. **hint: pick a number close to 1 from the right

Ex) Find the limit analytically. **hint: pick a number close to 3 from the right

Def: If f(x) approaches as x approaches c from the right or the left, then the line x=c is a vertical asymptote of f(x). **The vertical asymptote occurs at a number at which the denominator is 0 and the numerator is not 0.

Ex) Find the vertical asymptotes (if any) of the graph of each function. Then describe the behavior of the function on either side of the asymptote.

Ex) Find the vertical asymptotes (if any) of the graph of each function. Then describe the behavior of the function on either side of the asymptote.