PreCalc CH 12.4 Limits at Infinity and Limits of Sequences.notebook
PreCalc CH 12.4 Limits at Infinity and Limits of Sequences.notebook
Limits at Infinity and Limits of Sequences
April 10, 2013
Limits at Infinity and Limits of Sequences
Definition of Limits at Infinity If f is a function and L1 and L2 are real numbers, the statements:
denote the limits at infinity.
Limits at Infinity and Limits of Sequences
Limits at Infinity and Limits of Sequences Limits at Infinity:
As seen in the previous graph, when we find the limit at infinity, we are finding the horizontal asymptote of the graph.
If r is a positive real number, then:
Think about what is happening to the denominator as x approaches positive or negative infinity.
Limits at Infinity and Limits of Sequences Find the limit.
Limits at Infinity and Limits of Sequences Find the limit.
1
PreCalc CH 12.4 Limits at Infinity and Limits of Sequences.notebook
Limits at Infinity and Limits of Sequences
April 10, 2013
Limits at Infinity and Limits of Sequences
Here is a limit where we already have seen the answer, but not the equation which produced our answer.
Limits at Infinity and Limits of Sequences When we looked at horizontal asymptotes earlier in the year, we compared the degree of the numerator and denominator to determine the horizontal asymptotes. Now we will examine horizontal asymptotes using the limit process with rational functions. We will compare the degree of the numerator to the degree of the denominator.
Limits at Infinity and Limits of Sequences
Limits at Infinity and Limits of Sequences If the degree of the numerator is less than the degree of the denominator, then the limit of the rational function is 0.
Limits at Infinity and Limits of Sequences If the degree of the numerator is equal to the degree of the denominator, then the limit of the rational function is the ratio of the leading coefficients.
2
PreCalc CH 12.4 Limits at Infinity and Limits of Sequences.notebook
Limits at Infinity and Limits of Sequences
April 10, 2013
Limits at Infinity and Limits of Sequences If the degree of the numerator is greater than the degree of the denominator, then the limit of the rational function does not exist.
the limit does not exist.
Limits at Infinity and Limits of Sequences
3
Limits at Infinity and Limits of Sequences
April 10, 2013
Limits at Infinity and Limits of Sequences
Definition of Limits at Infinity If f is a function and L1 and L2 are real numbers, the statements:
denote the limits at infinity.
Limits at Infinity and Limits of Sequences
Limits at Infinity and Limits of Sequences Limits at Infinity:
As seen in the previous graph, when we find the limit at infinity, we are finding the horizontal asymptote of the graph.
If r is a positive real number, then:
Think about what is happening to the denominator as x approaches positive or negative infinity.
Limits at Infinity and Limits of Sequences Find the limit.
Limits at Infinity and Limits of Sequences Find the limit.
1
PreCalc CH 12.4 Limits at Infinity and Limits of Sequences.notebook
Limits at Infinity and Limits of Sequences
April 10, 2013
Limits at Infinity and Limits of Sequences
Here is a limit where we already have seen the answer, but not the equation which produced our answer.
Limits at Infinity and Limits of Sequences When we looked at horizontal asymptotes earlier in the year, we compared the degree of the numerator and denominator to determine the horizontal asymptotes. Now we will examine horizontal asymptotes using the limit process with rational functions. We will compare the degree of the numerator to the degree of the denominator.
Limits at Infinity and Limits of Sequences
Limits at Infinity and Limits of Sequences If the degree of the numerator is less than the degree of the denominator, then the limit of the rational function is 0.
Limits at Infinity and Limits of Sequences If the degree of the numerator is equal to the degree of the denominator, then the limit of the rational function is the ratio of the leading coefficients.
2
PreCalc CH 12.4 Limits at Infinity and Limits of Sequences.notebook
Limits at Infinity and Limits of Sequences
April 10, 2013
Limits at Infinity and Limits of Sequences If the degree of the numerator is greater than the degree of the denominator, then the limit of the rational function does not exist.
the limit does not exist.
Limits at Infinity and Limits of Sequences
3
