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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 22

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online