Unknown
Hints^243 Look at x2 - y2 and xy. The local extrema are those k for which y = k is tangeut to the graph of the cubic. 2(ab - cd ...
Answers to Exercises and Solutions to Problems Answers to Exercises Chapter 1 1.1. (a) 5, 1, 0, 7; (b) 5, 3, 2, 8; (c) 3, 0, 0, ...
Answers to Exercises; Chapter 1 245 Alternatively, the identical vanishing of p(t) implies the same for all of its derivatives, ...
246 Answers to Exercises and Solutions to Problems Hence, p(t) has a single term, and it can be seen that the polynomials commut ...
Answers to Exercises; Chapter 1 247 2.16. The abscissae 21 and 22 of the endpoints of the chord y = mx + k are the roots of the ...
248 Answers to Exercises and Solutions to Problems The treasure is located at (l/2)( l+ 1 ‘) , midway between P and Q. Since thi ...
Answers to Exercises; Chapter 1 249 (d) By de Moivre’s Theorem, cosn0 + isin n0 n n = cc > cos”-* e sins Oi* S a=0 n = Y( ) 2 ...
250 Answers to Exercises and Solutions to Problems 4.9. p3+8q2 = 0. If y = 2x, the latter equation becomes y4 = (~~+6y-18)~. 4.1 ...
Answers to Exercises; Chapter (^1 251) 5.1. Homogeneous: (a), (b), (e), (f); Symmetric: (c). 5.2. The “only if’ part is straight ...
252 Answers to Exercises and Solutions to Problems representation of n as a product of primes, or n/p1 < n, and we can ap- pl ...
Solutions to Problems; Chapter 1 253 = sin2(A + B) + (q - 1) tan(A + B) sin(A + B) cos(A + B) + q cos2(A + B) = sin2(A + B) + qs ...
254 Answers to Exercises and Solutions to Problems from which the result follows. 8.6. The quadratics all have the form x2 + ux ...
Solutions to Problems; Chapter 1 255 from which the result follows. 8.14. (a) The quadratic equation can be rewritten (z - u)~ = ...
256 Answers to Exercises and Solutions to Problems It4 - i] = 121 - i] = J4cos2 e + 2sin #I = Jz. Hence u and v lie on a circle ...
Solutions to Problems; Chapter (^1 257) where tan+ = (a - b)/2h. The maximum (minimum) occurs when sin(20 + 4) is equal to 1 (-1 ...
258 Answers to Exercises and Solutions to Problems a from the last two inequalities yields respectively -6 5 a - 2c 5 6 and -5 5 ...
Solutions to Problems; Chapter 1 259 Take u2 + v2 = 3x - 4. Then 2u2 = 2x - 3, 2v2 = 42: - 5. If 3: < 514, the square roots a ...
260 Answers to Exercises and Solutions to Problems have degree 3. No polynomial has a term in x3, y3 or z3, for such terms would ...
Solutions to Problems; Chapter 1 261 From the recursion relation, (Y + zPn(x, Y, z + 1) - (x + Y)P*(X + 1, Y, 4 + (2 - z>Pn(x ...
262 Answers to Exercises and Solutions to Problems If T = 1, there are f(n - 1) ways of choosing al,... ,a,-1 to satisfy inequal ...
«
9
10
11
12
13
14
15
16
17
18
»
Free download pdf