Thomas' Calculus (14th Edition)
14th Edition
ISBN: 9780134438986
Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher: PEARSON
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Chapter A.7, Problem 28E
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43–46. Directions of change Consider the following functions f and
points P. Sketch the xy-plane showing P and the level curve through
P. Indicate (as in Figure 15.52) the directions of maximum increase,
maximum decrease, and no change for f.
■ 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)
plese do #48
43-46. Directions of change Consider the following functions f and
points P. Sketch the xy-plane showing P and the level curve through
P. Indicate (as in Figure 15.52) the directions of maximum increase,
maximum decrease, and no change for f.
T 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)
Chapter A.7 Solutions
Thomas' Calculus (14th Edition)
Ch. A.7 - Find the following products of complex numbers
(2...Ch. A.7 - Solve the following equations for the real...Ch. A.7 - How may the following complex numbers be obtained...Ch. A.7 - Show that the distance between the two points z1...Ch. A.7 - graph the points z = x + iy that satisfy the given...Ch. A.7 - Prob. 6ECh. A.7 - graph the points z = x + iy that satisfy the given...Ch. A.7 - graph the points z = x + iy that satisfy the given...Ch. A.7 - graph the points z = x + iy that satisfy the given...Ch. A.7 - graph the points z = x + iy that satisfy the given...
Ch. A.7 - Prob. 11ECh. A.7 - Express the complex numbers in Exercises 11–14 in...Ch. A.7 - Prob. 13ECh. A.7 - Prob. 14ECh. A.7 - Prob. 15ECh. A.7 - Prob. 16ECh. A.7 - Find the three cube roots of 1.
Ch. A.7 - Find the two square roots of i.
Ch. A.7 - Find the three cube roots of –8i.
Ch. A.7 - Prob. 20ECh. A.7 - Find the four solutions of the equation z4 – 2z2 +...Ch. A.7 - Find the six solutions of the equation z6 + 2z3 +...Ch. A.7 - Find all solutions of the equation x4 + 4x2 + 16 =...Ch. A.7 - Prob. 24ECh. A.7 - Prob. 25ECh. A.7 - Prob. 26ECh. A.7 - Prob. 27ECh. A.7 - Prob. 28ECh. A.7 - When If z and are equal, what can you say about...Ch. A.7 - Real and imaginary parts Let Re(z) denote the real...
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- The Cartesian coordinates of a point are given. (a) (-8, 8) (i) Find polar coordinates (r, 0) of the point, where r > 0 and 0 ≤ 0 0 and 0 ≤ 0 < 2π. (1, 0) = (r. = ([ (ii) Find polar coordinates (r, 8) of the point, where r < 0 and 0 ≤ 0 < 2π. (5, 6) = =([arrow_forwardThe Cartesian coordinates of a point are given. (a) (4,-4) (i) Find polar coordinates (r, e) of the point, where r > 0 and 0 0 and 0 < 0 < 2π. (r, 6) = X 7 (ii) Find polar coordinates (r, 8) of the point, where r < 0 and 0 0 < 2π. (r, 0) = Xarrow_forwardr>0 (r, 0) = T 0 and one with r 0 2 (c) (9,-17) 3 (r, 8) (r, 8) r> 0 r<0 (r, 0) = (r, 8) = X X X x x Warrow_forward
- 74. Geometry of implicit differentiation Suppose x and y are related 0. Interpret the solution of this equa- by the equation F(x, y) = tion as the set of points (x, y) that lie on the intersection of the F(x, y) with the xy-plane (z = 0). surface Z = a. Make a sketch of a surface and its intersection with the xy-plane. Give a geometric interpretation of the result that dy dx = Fx F χ y b. Explain geometrically what happens at points where F = 0. yarrow_forwardExample 3.2. Solve the following boundary value problem by ADM (Adomian decomposition) method with the boundary conditions მი მი z- = 2x²+3 дг Əz w(x, 0) = x² - 3x, θω (x, 0) = i(2x+3). ayarrow_forward6. A particle moves according to a law of motion s(t) = t3-12t2 + 36t, where t is measured in seconds and s is in feet. (a) What is the velocity at time t? (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) What is the acceleration at time t? (f) What is the acceleration after 3 s?arrow_forward
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