Limits Review (Sections 10.1 – 10.3) Pre-Calculus

Asymptotes Asymptote Condition Vertical Denominator = 0 Horizontal when n < m when n = m when n > m y = 0 y = an/am none Slant when n > m by exactly 1 Divide numerator by denominator Pre-Calculus

Chapter 10 Review #1 – 14 19 – 26 (skip 6, 10, 23, 24) (p. 794) Due 5/28 #1 – 14 19 – 26 (skip 6, 10, 23, 24) (p. 794) Pre-Calculus

10.3 Limits Day # 1 Pre-Calculus

Inputs approach 2 from the left Inputs approach 2 from the right x = 2 2 Inputs approach 2 from the left Inputs approach 2 from the right x f(x) 1.9 1.99 1.999 2.001 2.01 2.1 2.9256 2.9925 2.9992 3.0007 3.0075 3.0756 Outputs approach 3 3 Outputs approach 3 Pre-Calculus

f(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a. seeing how the values of a function f(x) approach a value L (Limit) as x approaches the value a. Pre-Calculus

10.3 Limits Day # 2 Pre-Calculus

The limit of f as x approaches c from the left left-hand limit right-hand limit The limit of f as x approaches c from the left The limit of f as x approaches c from the right Pre-Calculus

A function f(x) has a limit as x approaches c iff the left-hand and two – sided limit A function f(x) has a limit as x approaches c iff the left-hand and right-hand limits at c exist and are equal. That is, Pre-Calculus

the greatest integer less than or equal to x does not exist discontinuous step – function the greatest integer less than or equal to x 2 1 – 2 1 2 does not exist Pre-Calculus

True True True False False False True False True False True True True False False False True False True False Pre-Calculus

10.3 Limits Day # 3 Pre-Calculus

Does not exist Pre-Calculus

Does not exist – constantly fluctuates between 1 and -1 Pre-Calculus

From Chapter 2 denominator quotient output input the x – axis ( y = 0 ) the line y = an / bm there is no quotient output input Pre-Calculus

Chapter 8 Review #4, 10, 12, 13 – 20, 24, 38 – 48 even (p. 664) Due 5/25 #4, 10, 12, 13 – 20, 24, 38 – 48 even (p. 664) Pre-Calculus