MAT 127 Midterm: mt1s09sol

23 views3 pages

turquoisegnu128

31 Jan 2019

School

University of Maine

Department

Mathematics and Statistics

Course

MAT 127

Professor

All

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

April 19, 2016: (20 pts) compute the following. (a) z sin(cos x) sin(x)dx. Let u = cos(x), du = sin(x)dx. Z sin(cos x) sin(x)dx = z sin(u)du = cos(u) + c = cos(cos(x)) + c. (b) z 1. Use ibp with u = x, dv = exdx, v = ex. [(2x 1)16 + 1 (1 2x)]dx = z 1. + x2(cid:12)(cid:12) (1 ( 1)17) + 1 = 17: (20 pts) in this problem you will show how to compute the number up to 10 decimal places. (a) show that z 1. 0 = 4 arctan(1) 4 arctan(0) = 4( /4) 4(0) = . (b) use simpson"s rule with n = 4 to approximate . Your answer should be a sum of numbers, but do not simplify. [f (0) + 4f (1/4) + 2f (1/2) + 4f (3/4) + f (1) One can show (with a computer) that this simpli es to s4 = 8011.

Related Questions

[1] 1. (a) Solve 2 – 31 < 7. Solution: We have – 7<-3 < 7 which gives -4 0 on (-0, 1] U [2,). Next, we need to see where Vr2 – 3r +2 -1 > 0. If r2 - 3.c + 2 – 1 > 0, then V.22 – 3.0 +2 > . Observe that this is definitely true if r < 0. If r > 0, then squar- ing both sides we get 22 - 3.+2 > 1 2 > 3. V A VICO Thus, the domain of f is (-00, ). [2] (c) Find the exact value of tan(sec-14). Solution: Let y = sec-14. Then, sec y = 4. From the diagram we get that tan(sec-? 4) = tan y = 15 [2] (d) Find all r such that sin(2.x) = COS I. Solution: We have 2 sin r cos r = COS I, SO 0 = 2 sin Cos I -Cos I = cos .r (2 sin c - 1). Hence, sin(2x) = cost when cos x = 0, or when sin r = Thus, r= +ik, kez, I= +2nk, ke Z, or r= +2nk, kez [2] (e) State the precise mathematical definition of lim f(x) = 0. Solution: For every e > 0 there exists a 8 >0 such that if 0 < x-al <, then f(c) >

MAT 127 Midterm: mt1s09sol

Document Summary

Get access

Related Documents

MAT 127 Midterm: S16mt1sol

MAT 127 Midterm: S07mt2sol

Related Questions