FDWKCalcSM_ch10

FDWKCalcSM_ch10 - Section 10.1 421 70. Continued Multiply...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 10.1 421 70. Continued Multiply by x . nn x x x n n () += = 1 2 1 3 1 Replace x by 1 x . x x x x x x n n , + = = > = 1 2 1 1 2 1 1 1 3 2 3 (b) Solve to get for x x x xx = ≈> 2 1 2 769 1 2 3 .. 71. (a) Computing the coefficients, f fx x f ( ) , ( 1 1 2 11 1 4 2 2 = =− + =− ′′ = so x f x + = ′′′ + 1 1 2 1 8 61 3 4 ), ! ( so so = + f f n n ! , ! . 1 3 1 16 1 2 1 In general S o x n n n + ++ + + 1 2 1 4 1 8 1 1 2 2 1 ±± (b) Ratio test for absolute convergence: lim n n n n n x x x →∞ + + + = 1 2 2 1 1 2 1 2 1 i x x <⇒−< < 1 2 3 . The series converges absolutely on( , ) . 13 At the series is which diverges by th x n = 1 1 2 0 ,, e th-term test n . At the series is which diverges x n n = 31 1 2 0 ,( ) , by the th-term test n . The interval of convergence is ( 1, 3). (c) Px 3 2 1 2 1 4 1 8 + P 3 2 05 1 2 05 1 4 8 0 65265 (.) .( . ) . + = 72. (a) Ratio test for absolute convergence: lim lim n n n n n n nx n n x →∞ + + →∞ + = + = 1 2 21 22 2 1 1 i 12 2 x The series converges absolutely on ( 2, 2). The series diverges at both endpoints by the n th-term test, since lim lim ( ) . n →∞ →∞ ≠− 01 0 and The interval of convergence is ( 2, 2). (b) The series converges at 1 and forms an alternating series: −+−+ + − + 1 2 2 4 3 8 4 16 1 2 . n n n The n th-term of this series decreases in absolute value to 0, so the truncation error after 9 terms is less than the absolute value of the10 th term. Thus error << 10 2 001 10 73. (a) x 1 (b) x x 2 2 3 2 (c) x x x 3 23 3 2 2 3 + (d) P 3 07 1 207 3 2 2 3 + Chapter 10 Parametric, Vector, and Polar Functions Section 10.1 Parametric Functions (pp. 531–537) Exploration 1 Investigating Cycloids 1. [0, 20] by [–1, 8] 2. xn a = 2 π for any integer n. 3. at y >− 0 0 and so cos . 4. An arch is produced by one complete turn of the wheel. Thus, they are congruent. 5. The maximum value of y is 2 a and occurs when a =+ for any integer n. 6. The function represented by the cycloid is periodic with period 2 a , and each arch represents one period of the graph. In each arch, the graph is concave down, has an absolute maximum of 2 a at the midpoint, and an absolute minimum of 0 at the two endpoints. Quick Review 10.1 1. tx yt x x =+= −+= + 1 232 132 1 2. t x x x = = −= 3 54 3 54 3 32 3 3 3 3
Background image of page 1

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

View Full DocumentRight Arrow Icon
422 Section 10.1 3. xt yt tt xy 22 1 1 = = += sin cos cos sin 4. ytt t yx == = sin sin cos 2 5. x y x 2 1 1 = = =+ tan sec sec tan θ 6. x y 2 1 1 + = csc cot cot θθ 7. x y 2 2 1 21 = =− cos cos cos 8. x y 2 2 2 12 = sin cos sin 9. x y 2 2 1 10 = ≤≤ cos sin cos ,( ) θπ 10. x y 2 2 1 = ≤ ≤ cos sin cos ) πθ π Section 10.1 Exercises 1. Yes, y is a function of x. 29 (3, –3) (9, 9) 1 10 10 1 –3 0 x y 2. Yes, y is a function of x. y x = + 2 7 4 (1, 2) (3, 4) 1 5 1 0 x y 4 3. Yes, y is a function of x . 2 1 (1, 0) (2, 1.732) 3 3 1 0 x y 4. No, y is not a function of x. x y 2 2 4 1 (0, 2) (0, –2) 3 1 –3 –1 x y 5. Yes, y is a function of x.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/26/2010 for the course MATH 135 taught by Professor Noone during the Summer '08 term at Rutgers.

Page1 / 24

FDWKCalcSM_ch10 - Section 10.1 421 70. Continued Multiply...

This preview shows document pages 1 - 3. Sign up to view the full document.

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