Q1] Find the derivative of f(x, y) = x2e-2y at po (1,2) in the direction of v =i+j. In what directions does f change most rapidly at p, and what are the rates of change in these directions? %3D Q2] (Choose only one) a) Use the Chain rule to find the derivative of z e*y with respect tot along the path x t cost and y =t sin t. What is the derivative's value at t n/2 az and ax az b) Find given that xy + z + sin(xyz) = 0. ay Q3] For the following integrals, write an equivalent double integral with the order of integration reversed. r1 (3-2x a) So S f(x,y) dydx (8 Marks) b) S S, F(x, y) dxdy (7 Marks) Q4] Use double integrals to find the area of the region that lies inside the cardioid r = 1+ cos 0 and outside the circle r =1.

Q1] Find the derivative of f(x, y) = x2e-2y at po (1,2) in the direction of v =i+j. In what directions does f change most rapidly at p, and what are the rates of change in these directions? %3D Q2] (Choose only one) a) Use the Chain rule to find the derivative of z e*y with respect tot along the path x t cost and y =t sin t. What is the derivative's value at t n/2 az and ax az b) Find given that xy + z + sin(xyz) = 0. ay Q3] For the following integrals, write an equivalent double integral with the order of integration reversed. r1 (3-2x a) So S f(x,y) dydx (8 Marks) b) S S, F(x, y) dxdy (7 Marks) Q4] Use double integrals to find the area of the region that lies inside the cardioid r = 1+ cos 0 and outside the circle r =1.

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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