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Clicker Question 1

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

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  1. Clicker Question 1 • Solve: x2 = 28 – 3x • (28 – 3x) • 7 and -4 • -7 and 4 • 0 and 3 • 28 and -3

  2. Clicker Question 2 • Solve: arctan(3x2) = /4 • A. 1 only • B. 1/3 only • C.  1/3 • D.  1 • E. (/12)

  3. 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.

  4. Examples • limx   1/(x + 4) = • limx  x + 4 = • limx  -x + 4 = • limx   ex = • limx  - ex = • limx   arctan(x ) = • limx   (2x +3)/(x – 1) =

  5. 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) =

  6. Clicker Question 3 • What is limx   x / (x2 +5) ? • A. +  • B. -  • C. 0 • D. 1 • E. Does not exist

  7. Clicker Question 4 • What is limx   x 2/ (x2 +5) ? • A. +  • B. -  • C. 0 • D. 1 • E. Does not exist

  8. Clicker Question 5 • What is limx  - x 3/ (x2 +5) ? • A. +  • B. -  • C. 0 • D. 1 • E. Does not exist

  9. 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?

  10. 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.

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