MAT 127 Midterm: mt2sols09

23 views4 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 3, 2009: (30 pts) compute the following integrals. Z sec2 d = tan + c. Z cos3(x) sin4(x)dx = z cos2(x) sin4(x) cos(x)dx = z (1 sin2(x)) sin4(x) cos(x)dx. = z (1 u2)u4du = z (u4 u6)du = u5. 2: (20 pts) griswald puts a frozen hot dog into a pot of boiling water. The temperature of the hot dog at time t = 0 is 0 c. After 2 minutes, the hot dog is 5 c. (a) by newton"s law of cooling, the rate of change of the temperature of the hot dog is proportional to the di erence in temperature between the water and the hot dog. We let y = y(t) denote the temperature at time t. dy dt. = k(100 y), y(0) = 0, y(2) = 5. (b) solve the ivp to obtain the temperature of the hot dog at time t. 100 y dy = k dt = z.

Related Questions

I am hoping to solve a derivatives example, but Iâm confused on how to use the rules the example question was f(x)=-4x^2ln(4x^3 -x^2)

Show transcribed image text

bronzehornet861

integrate the following functions :

1. cos^5(x) * sin^6(x) dx

2. tan^5(x) * sec^6(x) dx

3. tan^5(x) * sec^7(x) dx

4. Use techniques of trig substitution to solve following integral: x * (4 + x ^2)^0.5 dx

5. Use techniques of trig substitution to solve following integral: x * (4 â x ^2)^0.5 dx

[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: mt2sols09

Document Summary

Get access

Related Documents

MAT 127 Midterm: mt1s09

MAT 127 Midterm: S06mt2sol

MAT 127 Final: S06final

Related Questions