MTH 140 Chapter Notes - Chapter 9: Verb, Qi, Nsb El 13

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mauvefish953

8 Aug 2018

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1 . - -~ . - ::. u Cor w5ic>le - the non-"lineor diff eq- linear, ffsb order is colleql norw-linear} (see ch- 10)" =0 [5 5o ol id be jg, /obie or y car-7 be pm: i. Putgng value o{ " 5" q9- @, we. get. Tf. e. diff-~ . fit c "" t b %fq<1torizeok "o1rwol com be. :1=xp1- (p3 - : w. ,-. t if we get " . 4 i{ we c. or"\sioler x+ (p3 = if we. consider. I pukl-{mg in eq- { the above theorem we get. Tqpfe"5e( b thq,"~ if\9lllof sol ojr~ involves no orbiffad ""5 """ "e "" 5""9"~ o" sown . We can eh"mi"nol- p {row-@, <1: (_1)}"-5 ti"_= *3/l1("x)q/3. 6h 9 + 3>l =_ o req- 5. -@9111; sol. Eh"-qhiop sol. s- _. zf\( v u_jn. ,(%\/td av. J/qnce becomes, r uh = "2q/ y = w1-1w =-w1 1"-ff @

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[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) >

Calculate the scalar triple product u dot (v x w), where u = <1, 1, 0>, v= <3, -2, 2>, and w= <4, -1, 2>.

MTH 140 Chapter Notes - Chapter 9: Verb, Qi, Nsb El 13

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