# ch03 - Chapter 3 Introduction to Calculus Review of...

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Review of Prerequisite Skills 2. e. The slope of line is The equation of the line is in the form . The point is and . The equation of the line is or . 4. a. b. c. 6. b. d. g. 53 23 4 30 20 3 12 16 30 20 3 4 10 3 15 2 + × = = = 1 33 93 6 + × = = 62 3 3 3 63 6 3 + ×= + f 78 9 () = f 03 = f –33 6 = fx xx = < +≥ 30 –i f if 653 6 0 xy += yx –6 6 5 1 =+ m = 6 5 –, 16 yy m –– 11 = m = = 12 6 41 6 5 7. b. c. d. f. 8. h. i. Therefore, is a factor. By division, the other factor is . Therefore, 9. j. The domain is k. The domain is xR x ∈= ,– , . 1 2 3 and y x x = = + ( ) 6 25 3 6 21 3 2 x ∈≠ ,, . or y = = + 7 34 7 2 27 6 1 2 6 12 3 2 32 2 xx x x x . + = ( ) + 26 2 + x –1 6 12176 0 f + = xxx x x x 2 2 23 6 2 ––– + = + 7 5 7 7 12 7 10 3 5 7 5 10 3 5 7 + × == 23 5 12 25 66 1 52 13 × + + = + = + 74 5 71 6 57 2 0 9 0 × + + = + = + 3 3 3 3 6 + + Chapter 3: Introduction to Calculus 51 Chapter 3 • Introduction to Calculus

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Section 3.1 Investigation 1 1. 2. Slope of secant P (3, 9), Q i : 3. 4. Slope of the tangent at P (3, 9) seems to be 6. Investigation 2 3. Slope Slope Slope Slope Slope 5. Slope of the tangent at P (1, 1) is 2. Investigation 3 1. Slope of PQ = + () + = ++ =+ 39 33 96 9 60 2 2 h h hh h , PQ 3 3 2 ,, ()++ PQ f 5 1 0001 1 0001 2 0001 ., . . = PQ f 4 1 001 1 001 2 001 ., . . = PQ f 3 101 201 . = PQ f 2 11 21 . . = PQ 1 25 . f 15 1 ,, . , . ( ) PQ PQ PQ PQ 5 6 7 8 55 59 599 5 999 . . . . a. b. c. d. QQ 5 6 7 8 25 625 29 841 2998 9401 2 999 8 994001 .,. . . , . ( ) PQ PQ PQ PQ 1 2 3 4 65 61 601 6 001 . . . . a. b. c. d. 12 34 351225 31961 3019 0601 3 001 9 00600 . . ()( ) ( ) yx = 2 52 Chapter 3: Introduction to Calculus 2. Substitute in the above slope. Exercise 3.1 4. b. c. d. e. f. g. 5. a. b. h hh h h 22 2 2 54 2 4 2 5 2 = +++ = + –– 16 4 16 16 16 4 1 16 4 + = + = h h h h 3 4 3 4 12 12 3 44 3 + = = + h h h h h h 28 2 2 2 4 12 6 3 2 2 + = + + + =++ h h hhh h 31 3 1 31 2 1 32 63 2 2 2 2 + = + = = + h h h h h h h 1 1 1 1 1 1 + = + = + h h h h 38 1 996 9 8 6 108 54 12 4 2 23 + = + + + = + + h h h h h h 5 125 5 5 5 2 5 75 15 75 15 3 2 2 2 + = + + + = =+ + h h h h h h = 0
c. 6. a. b. c. 7. a. PQ Slope 19 15.25 12.61 12.0601 (1, 1) 7 9.25 11.41 11.9401 1997 880599 ., . () 19 6859 .,. 15 3375 ., . 2018 120601 21 9261 25 15 625 327 , 28 , m h h h h h = + ++ = 93 1 TU h h 9 9 ,, , ()++ m h h hhh h hh = + + = ++ + =+ + 12 3 13 3 1 33 3 23 2 RS h h 13 1 1 2 3 , + m h h h = + =+ 31 3 63 2 h f h f x x 1 1 3 2 , , ( ) = 55 5 5 1 + = + = h h h h –– 8. a. at c. at 9. a. ; (3, 1) at m h h h h h h h h h h = + = + × = = lim lim lim 0 0 0 95 2 42 1 1 4 xy == 92 , yx = –5 m h h h h h h h h h h = + = + × = = lim lim lim 0 0 0 32 1 11 1 1 2 = –2 m h h h h h h = + + = + = lim lim lim 0 3 0 0 2 81 2 6 8 12 6 12 –, = 3 m h h h h h h h = + + = = lim lim ––– lim 0 2 0 2 0 6 96 3 6 5 5 36 , yx x = 2 m h h h h h h h = + = + = lim lim lim – 0 2 0 2 0 1 2 12 12 3 12 12 3 12 = 1 2 2 ,–, Chapter 3: Introduction to Calculus 53

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c. at 10. a. at (2, 4) b. at ; c. at ; m h h h h h = + = + () = lim lim 0 0 1 5 1 5 1 55 1 10 y = 1 5 x = 3 y x = + 1 2 m h h h h h = + = + = lim lim 0 0 8 4 2 2 4 1 2 y = 2 x = 1 y x = + 8 3 lim lim lim xh h x x m h h h →→ = + = + = 50 0 5 5 8 2 4 4 2 2 y x = 8 m h h h h h h h h h h = + = + × ++ = = lim –– lim lim 0 0 0 10 5 1 3 95 3 95 3 95 3 5 5 6 xy == 23 , yx = 51 11. a.
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## This note was uploaded on 02/10/2010 for the course MATHS MCV-01 taught by Professor Mr.m during the Spring '10 term at Seneca.

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ch03 - Chapter 3 Introduction to Calculus Review of...

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