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Clicker Question 1. Solve: x 2 = 28 – 3 x (28 – 3 x ) 7 and -4 -7 and 4 0 and 3 28 and -3. Clicker Question 2. Solve: arctan(3 x 2 ) = /4 A. 1 only B. 1/3 only C. 1/3 D. 1 E. (/12). Limits at Infinity (10/25/10).
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Clicker Question 1 • Solve: x2 = 28 – 3x • (28 – 3x) • 7 and -4 • -7 and 4 • 0 and 3 • 28 and -3
Clicker Question 2 • Solve: arctan(3x2) = /4 • A. 1 only • B. 1/3 only • C. 1/3 • D. 1 • E. (/12)
Limits at Infinity (10/25/10) • By the “limit at infinity of a function f″ we mean what f ′s value gets near as the input x goes out the positive (+) or negative (-) horizontal axis. • We write limx f (x ) or limx - f (x ). • It’s possible that the answer can be a number, or be or -, or not exist.
Examples • limx 1/(x + 4) = • limx x + 4 = • limx -x + 4 = • limx ex = • limx - ex = • limx arctan(x ) = • limx (2x +3)/(x – 1) =
Algebraic Quotients Going to over • As x, the quotient of two algebraic functions will approach the ratio of the highest degree terms top and bottom. • Examples: • limx (2x +3)/(x – 1) = • limx (2x +3)/(x2 – 1) = • limx (x3 – 4x +3)/(x – 1) =
Clicker Question 3 • What is limx x / (x2 +5) ? • A. + • B. - • C. 0 • D. 1 • E. Does not exist
Clicker Question 4 • What is limx x 2/ (x2 +5) ? • A. + • B. - • C. 0 • D. 1 • E. Does not exist
Clicker Question 5 • What is limx - x 3/ (x2 +5) ? • A. + • B. - • C. 0 • D. 1 • E. Does not exist
Nonexistent Limits at Infinity? • Is it possible for a function to have no limit at infinity (including not + nor -)? • If so, what is an example?
Assignment for Wednesday • Section 2.6 goes into more detail than we really need. Read it as needed but definitely study and understand the class notes. • In Section 2.6 (page 140-1), do Exercises 1, 3, 7, 9, 15, 19, 28, 31, 35.