Essential Calculus: Early Transcendentals
2nd Edition
ISBN: 9781133112280
Author: James Stewart
Publisher: Cengage Learning
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Chapter B, Problem 14E
To determine
To write: The sum
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please 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.
■ 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)
plese do #48
Chapter B Solutions
Essential Calculus: Early Transcendentals
Ch. B - Prob. 1ECh. B - Write the sum in expanded form. 2. i=161i+1Ch. B - Write the sum in expanded form. 3. i=463iCh. B - Write the sum in expanded form. 4. i=46i3Ch. B - Write the sum in expanded form. 5. k=042k12k+1Ch. B - Write the sum in expanded form. 6. k=58xkCh. B - Write the sum in expanded form. 7. i=1ni10Ch. B - Write the sum in expanded form. 8. j=nn+3j2Ch. B - Write the sum in expanded form. 9. j=0n1(1)jCh. B - Write the sum in expanded form. 10. i=1nf(xi)xi
Ch. B - Write the sum in sigma notation. 11. 1 + 2 + 3 + 4...Ch. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - Prob. 15ECh. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Write the sum in sigma notation. 20. 1 x + x2 x3...Ch. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Find the value of the sum. 30. i=1n(25i)Ch. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Find the value of the sum. 35. i=1n(i3i2)Ch. B - Find the number n such that i=1ni=78.Ch. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prove the generalized triangle inequality:...Ch. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48ECh. B - Prob. 49ECh. B - Prob. 50E
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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. T 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)arrow_forwardSolve the differential equation by variation of parameters 3x2y" + 7xy' + y = x2 - xarrow_forward2 x² + 9 d x 1 x +9 dxarrow_forward
- DO these math problems without ai, show the solutions as well. and how you solved it. and could you do it with in the time spandarrow_forwardThe 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_forward
- r>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_forward74. 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_forward
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