Lesson 2 2 Limits as x approaches infinity

Lesson 2 -2: Limits as x approaches infinity Day #2 Mrs. Mongold AP Calculus

End Behavior Model • The function j is a. A right end behavior f if and only if b. A left end behavior f if and only if

Note • A functions right and left end behavior models need not be the same function. • Example: Finding End Behavior Models – Let f(x) = x+e-x – Show g(x)=x is a right end behavior model – While h(x)=e-x is a left end behavior model

SOLUTION

NOTE • If one function provides both left and right end behavior models it is simply called an end behavior model. • In general g(x)=anxn is an end behavior model for the polynomial function f(x)=anxn+an-1 xn-1+…+a 0, an≠ 0

Examples Finding End Behavior

NOTE • End behavior models can be used to identify any horizontal asymptotes

Example: Find a horizontal Asymptote

Example: Find vertical asymptote • We can say x=0 is the only vertical asymptote and that the limit is equal to 0 since LH=RH

End Behavior • For numerically large values of x, we can sometimes model the behavior of a complication function by a simpler one that acts virtually in the same way – f(x)=3 x 4 -2 x 3+3 x 2 -5 x+6 and g(x)=3 x 4 • While quite different for numbers that are small when |x| large they are virtually identical – Graphically different near origin but from same on larger scale

• Analytically

Homework • Pg 71 -73/ 3 -48 multiples of 3