Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 12.8, Problem 11PS
To determine
To find:The Jacobian
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Let f(x,y) =x -xy +y-y. Find the directions u and the values of D,f(1,- 1) for which the following is true.
a. Dyf(1, - 1) is largest
b. Duf(1,- 1) is smallest
c. Dyf(1, - 1)=0
d. Duf(1, - 1)=4
e. Duf(1, - 1)= -3
a. Find the direction u and the value of D,f(1,-1) for which D,f(1, - 1) is largest.
3.
i+
j and Duf(1, – 1) =D
u=
2. If ƒ(z) = z² − (z)² + zī, calculate the following:
a) u(x, y) and v (x, y)
b)
u(-10,-5) and v(-10,-5)
1. R= {(1, 1), (2, 2), (3, 4), (5,9)} C ZX Z
2. R= {(n, m) ENXZ: n² = m} CNXZ
3. R = {(n, m) EZXZ:m-n is even} C ZX Z
4. R = {(e, y): y ER} CRX R
15. R = {(x, y) €ERXR: P(x, y) is true} C R x R, where P(x, y) is the predicate
Chapter 12 Solutions
Calculus
Ch. 12.1 - Prob. 1PSCh. 12.1 - Prob. 2PSCh. 12.1 - Prob. 3PSCh. 12.1 - Prob. 4PSCh. 12.1 - Prob. 5PSCh. 12.1 - Prob. 6PSCh. 12.1 - Prob. 7PSCh. 12.1 - Prob. 8PSCh. 12.1 - Prob. 9PSCh. 12.1 - Prob. 10PS
Ch. 12.1 - Prob. 11PSCh. 12.1 - Prob. 12PSCh. 12.1 - Prob. 13PSCh. 12.1 - Prob. 14PSCh. 12.1 - Prob. 15PSCh. 12.1 - Prob. 16PSCh. 12.1 - Prob. 17PSCh. 12.1 - Prob. 18PSCh. 12.1 - Prob. 19PSCh. 12.1 - Prob. 20PSCh. 12.1 - Prob. 21PSCh. 12.1 - Prob. 22PSCh. 12.1 - Prob. 23PSCh. 12.1 - Prob. 24PSCh. 12.1 - Prob. 25PSCh. 12.1 - Prob. 26PSCh. 12.1 - Prob. 27PSCh. 12.1 - Prob. 28PSCh. 12.1 - Prob. 29PSCh. 12.1 - Prob. 30PSCh. 12.1 - Prob. 31PSCh. 12.1 - Prob. 32PSCh. 12.1 - Prob. 33PSCh. 12.1 - Prob. 34PSCh. 12.1 - Prob. 35PSCh. 12.1 - Prob. 36PSCh. 12.1 - Prob. 37PSCh. 12.1 - Prob. 38PSCh. 12.1 - Prob. 39PSCh. 12.1 - Prob. 40PSCh. 12.1 - Prob. 41PSCh. 12.1 - Prob. 42PSCh. 12.1 - Prob. 43PSCh. 12.1 - Prob. 44PSCh. 12.1 - Prob. 45PSCh. 12.1 - Prob. 46PSCh. 12.1 - Prob. 47PSCh. 12.1 - Prob. 48PSCh. 12.1 - Prob. 49PSCh. 12.1 - Prob. 50PSCh. 12.1 - Prob. 51PSCh. 12.1 - Prob. 52PSCh. 12.1 - Prob. 53PSCh. 12.1 - Prob. 54PSCh. 12.1 - Prob. 55PSCh. 12.1 - Prob. 56PSCh. 12.1 - Prob. 57PSCh. 12.1 - Prob. 58PSCh. 12.1 - Prob. 59PSCh. 12.1 - Prob. 60PSCh. 12.2 - Prob. 1PSCh. 12.2 - Prob. 2PSCh. 12.2 - Prob. 3PSCh. 12.2 - Prob. 4PSCh. 12.2 - Prob. 5PSCh. 12.2 - Prob. 6PSCh. 12.2 - Prob. 7PSCh. 12.2 - Prob. 8PSCh. 12.2 - Prob. 9PSCh. 12.2 - Prob. 10PSCh. 12.2 - Prob. 11PSCh. 12.2 - Prob. 12PSCh. 12.2 - Prob. 13PSCh. 12.2 - Prob. 14PSCh. 12.2 - Prob. 15PSCh. 12.2 - Prob. 16PSCh. 12.2 - Prob. 17PSCh. 12.2 - Prob. 18PSCh. 12.2 - Prob. 19PSCh. 12.2 - Prob. 20PSCh. 12.2 - Prob. 21PSCh. 12.2 - Prob. 22PSCh. 12.2 - Prob. 23PSCh. 12.2 - Prob. 24PSCh. 12.2 - Prob. 25PSCh. 12.2 - Prob. 26PSCh. 12.2 - Prob. 27PSCh. 12.2 - Prob. 28PSCh. 12.2 - Prob. 29PSCh. 12.2 - Prob. 30PSCh. 12.2 - Prob. 31PSCh. 12.2 - Prob. 32PSCh. 12.2 - Prob. 33PSCh. 12.2 - Prob. 34PSCh. 12.2 - Prob. 35PSCh. 12.2 - Prob. 36PSCh. 12.2 - Prob. 37PSCh. 12.2 - Prob. 38PSCh. 12.2 - Prob. 39PSCh. 12.2 - Prob. 40PSCh. 12.2 - Prob. 41PSCh. 12.2 - Prob. 42PSCh. 12.2 - Prob. 43PSCh. 12.2 - Prob. 44PSCh. 12.2 - Prob. 45PSCh. 12.2 - Prob. 46PSCh. 12.2 - Prob. 47PSCh. 12.2 - 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Prob. 3PSCh. 12.6 - Prob. 4PSCh. 12.6 - Prob. 5PSCh. 12.6 - Prob. 6PSCh. 12.6 - Prob. 7PSCh. 12.6 - Prob. 8PSCh. 12.6 - Prob. 9PSCh. 12.6 - Prob. 10PSCh. 12.6 - Prob. 11PSCh. 12.6 - Prob. 12PSCh. 12.6 - Prob. 13PSCh. 12.6 - Prob. 14PSCh. 12.6 - Prob. 15PSCh. 12.6 - Prob. 16PSCh. 12.6 - Prob. 17PSCh. 12.6 - Prob. 18PSCh. 12.6 - Prob. 19PSCh. 12.6 - Prob. 20PSCh. 12.6 - Prob. 21PSCh. 12.6 - Prob. 22PSCh. 12.6 - Prob. 23PSCh. 12.6 - Prob. 24PSCh. 12.6 - Prob. 25PSCh. 12.6 - Prob. 26PSCh. 12.6 - Prob. 27PSCh. 12.6 - Prob. 28PSCh. 12.6 - Prob. 29PSCh. 12.6 - Prob. 30PSCh. 12.6 - Prob. 31PSCh. 12.6 - Prob. 32PSCh. 12.6 - Prob. 33PSCh. 12.6 - Prob. 34PSCh. 12.6 - Prob. 35PSCh. 12.6 - Prob. 36PSCh. 12.6 - Prob. 37PSCh. 12.6 - Prob. 38PSCh. 12.6 - Prob. 39PSCh. 12.6 - Prob. 40PSCh. 12.6 - Prob. 41PSCh. 12.6 - Prob. 42PSCh. 12.6 - Prob. 43PSCh. 12.6 - Prob. 44PSCh. 12.6 - Prob. 45PSCh. 12.6 - Prob. 46PSCh. 12.6 - Prob. 47PSCh. 12.6 - Prob. 48PSCh. 12.6 - Prob. 49PSCh. 12.6 - Prob. 50PSCh. 12.6 - 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- 3. Compute feF · dr where F(x, y, z) = (x + yz, 2x, ryz) where C consists of the segments from (1,0, 1) to (2,3, 1) and from (2,3, 1) to (2,5, 2). (Answer: )arrow_forwardLet Compute dw əs Ow Ət (2, -3) = -(2,-3) = w = 4xy yz 3xz, x = st, y = est, z = ²arrow_forwardLet f(x,y) = x² - xy + y² − y. Find the directions u and the values of Df(1,-1) for which the following is true. b. Duf(1,-1) is smallest d. Duf(1,-1)=4 a. Duf(1,-1) is largest c. Duf(1,-1)=0 e. Duf(1,-1)=-3 a. Find the direction u and the value of Duf(1,-1) for which Duf(1,-1) is largest. u=arrow_forward
- W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. If u(3, 6) = -7, us (3,- 6) = 9, ut (3, 6) = 3, v(3, — 6) = 7, vs(3, — 6) = — 2, vt (3,6)= 5, Fu(-7, 7) -4, and F(-7, 7) = -3, then find the following: W,(3, 6) Wt(3, 6) =arrow_forward3. Evaluate Se(x² – iy²)dz along the straight lines from (1, 1) to (1, 8) and then from (1,8) to (2, 8).arrow_forward4.(2.5) Let g(x, y) = (x² + x, y + 3) and f(u, v) = (u – v, u² + v²). (1) Find Df(u, v) and Dg(x, y). (2) Find g(1, 1), Dg(1, 1) and D(f ○ g)(1, 1). 5.(2.6) (1) Let f(x, y) = ln(x² + y³) and v = derivative of f in the direction of v at x0 = (0, 1). Find Vf(x, y) and the directional 2 (2) Consider a curve given by x² - 2xy + y³ = 1. Find a normal vector to the curve at x0 = (2,1).arrow_forward
- 2. Sketch the level curve z = k for the indicated values of k.arrow_forwardIf x\y then gcd(x, y) = y. إختر واحداarrow_forwardExample: Calculate the value of (aw/@x) at the point (x, y, z) = (2,-1,1) if:- w = x2 + y2 + z? z3 – xy + yz +y3 = 0 Assuming that x and y are the independent variables.arrow_forward
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