Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Chapter 14.7, Problem 1PT
To determine
The appropriate option for the statement “A critical point of
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Find the midpoint between (8, 17) and (24, 31)
1. Differentiate: y = 3(²-1)
A. (In 3) 3(x²-1)
C. 2x (In 3) (3x²-1)
B. (2x) 3(x²-1)
D. x²(In 3)(3x²-1)
Let M(x) = 3x² – 5x + 2, find the following:
а) М(4)
b) м(-7)
c) M(c+ h) – M(c)
3.
Chapter 14 Solutions
Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 14.1 - Which of these points is not in the domain of...Ch. 14.1 - Prob. 2PTCh. 14.1 - Each level curve (for k 0) of f(x, y) = xy is...Ch. 14.1 - Prob. 4PTCh. 14.1 - The range of f(x,y)=x+1y is: a) (,) b) [0, ) c)...Ch. 14.2 - Prob. 1PTCh. 14.2 - Prob. 2PTCh. 14.2 - Prob. 3PTCh. 14.2 - Prob. 4PTCh. 14.2 - Prob. 5PT
Ch. 14.3 - fx(a, b) is the slope of the tangent line to the...Ch. 14.3 - Prob. 2PTCh. 14.3 - Prob. 3PTCh. 14.3 - Prob. 4PTCh. 14.3 - Prob. 5PTCh. 14.3 - Prob. 6PTCh. 14.4 - Prob. 1PTCh. 14.4 - Prob. 2PTCh. 14.4 - Prob. 3PTCh. 14.4 - Prob. 4PTCh. 14.5 - Prob. 1PTCh. 14.5 - Prob. 2PTCh. 14.5 - Prob. 3PTCh. 14.5 - Find zx for z=f(x,y) defined implicity by...Ch. 14.6 - Prob. 1PTCh. 14.6 - Prob. 2PTCh. 14.6 - For z = f(x, y) and u = j, Du f(a, b) = a) fx(a,...Ch. 14.6 - Prob. 4PTCh. 14.6 - Prob. 5PTCh. 14.6 - Prob. 6PTCh. 14.7 - Prob. 1PTCh. 14.7 - Prob. 2PTCh. 14.7 - Prob. 3PTCh. 14.7 - Prob. 4PTCh. 14.8 - Prob. 1PTCh. 14.8 - Prob. 2PT
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- 1. Differentiate. Do not simplify. b) g(x) = (7x3 – 3x² + x)(1 + 4x²) a) y = Vx4 -5x+1 с) у — d) g(x) = V7x² – 3x (2x2-3)3 e) f (x) = (2x² – 1)³(x* + 3)5arrow_forwardIf (x + y)² = u + iv, then show that "+"=(x² - y²). y Xarrow_forwardMaximize B=6xy2, where x and y are positive numbers such that x+y2=6.arrow_forward
- 2. If y = x2 + 2 and u = 2x – 1, then du 2x2-2x+4 (а) (2x-1)2 (b) 6х2 —2х + 4 (d) -arrow_forward1. Differentiate: 4.x (а) (b) x* – 6x +3 (c) (2x–1)Xx+2)(x-1) (d) Vx - x (e) 4x? 2.x? – x³ (f) 3.arrow_forwardFor u(x) = 4x2 - x + 5 and v(x) = 2x + 4, which of the following is correct? a) (u – v)(2) = 11 b) (u²) (3) = = 5329 c) (uv)(-4) = 780 d) (u) (4) = 1444arrow_forward
- 2. If Ā = î + ŷ, B = 2â – 3ŷ + î and C = 4ŷ – 32, determine - (a) (Ã × B) × Č (b) Ã× (B × Č) Comment on your answer.arrow_forward4) If f(x) = 3x - 2x + 5, find f(-2). A) -27 B) -11 C) -3 D) 21arrow_forward1. (2u). (2v) = 2 2. (7x+3y). (6x + 4y) = (u.v) Note: u. (vw) = u(v + (−1)w) =u.v+u.(-1)w =u.v + (-1)u.w =u.v-u.w, and similarly 3. (-4u) (6v - 2u) = 4. (3w - z). (w2z) = (X.X) + (vw).u=v.u-w. u. This means that the dot product is also distributive over vector subtraction. Using these additional properties, we can determine each of the following. (Some of the entries below could be negative numbers even though there is a + in front of them.) (u.u) + (x. y) + (w.w) + (u.v) + (y-y) (w.z) + (v.v) (z.z)arrow_forward
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