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Rate of Change of Function - Multivariable Calculus - Past Paper

Exams, Calculus

Post: February 11th, 2013
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These are the notes of Past Paper of Multivariable Calculus. Key important points are: Rate of Change of Function, Trigonometric Identities, Spherical Coordinates, Approximate Value, Numerical Values of Derivatives, Critical Points of Function, Tangent Plane
These are the notes of Past Paper of Multivariable Calculus. Key important points are: Rate of Change of Function, Trigonometric Identities, Spherical Coordinates, Approximate Value, Numerical Values of Derivatives, Critical Points of Function, Tangent Plane
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Contents
Name: Lab Section: MATH 215 – Fall 2004 FINAL EXAM Show your work in this booklet. Do NOT submit loose sheets of paper–They won’t be graded Problem Points Score 1 15 2 10 3 25 4 10 5 15 6 15 7 10 TOTAL 100 Some useful trigonometric identities: sin2 θ + cos2 θ = 1 1 − cos 2θ sin2 θ = 2 cos 2θ = cos2 θ − sin2 θ 1 + cos 2θ cos2 θ = 2 sin 2θ = 2 sin θ cos θ Spherical coordinates: x = ρ cos(θ) sin(φ) y = ρ sin(θ) sin(φ) z = ρ cos(φ) 1 Problem 1. (15 points) This problem is about the function f (x, y, z ) = 3zy + 4x cos(z ). (a) What is the rate of change of the function of f at (1, 1, 0) in the direction from this point to the origin? (b) Give an approximate value of f (0.9, 1.2, 0.11). CONTINUED ON THE NEXT PAGE 2 (c) Recall that f (x, y, z ) = 3zy + 4x cos(z ). The equation f (x, y, z ) = 4 implicitly defines z as a function of (x, y ), if we agree that z = 0 if (x, y ) = (1, 1). Find the numerical values of the derivatives ∂z ∂z (1, 1) and (1..

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