**1.** (a) Let \( f(x, y) = \cos(x + 4y) \). Compute the directional derivative \( D_{\mathbf{u}} f(x, y) \), where \( \mathbf{u} = \left\langle -\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right\rangle \).(b) Compute \(\iint_B x y^2 \, dA\), where \( B = [0, 1] \times [0, 3] \).

Answered: 1. (a) Let f(r,y)- cos(z + 2y). Compute…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Let g(z) = (23 + (z? - 1)5). Then the derivative of g is gʻe) = A(2? + (2? – 1)9)*(cP + F z(2? - 1)9), where + (z2 (? - 19)*(c zº + F z(z? - 1)9), where A = B : C = D = F = G =
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1. (a) Let f(r,y)- cos(z + 2y). Compute the diectional derivative Df(r,9), where u- (b) Compute ff, ry dA, where B (0, 1 0, 3.