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old calculus III exam with solutions to help you master the course and understand it more., Exams of Differential and Integral Calculus

Isik University Differential and Integral Calculus

*Preliminaries ( sphere, cylinders, quadratic surfaces) Multivariable functions. Limits. *Partial derivatives. The chain rules. implicit partial derivative. Directional Derivatives and Gradient Vectors. Tangent planes and differentials *Extreme Values and Saddle Points, Local maxima minima, Absolute maxima minima. * multipliers. Vector valued functions: their derivatives and integrals.

Typology: Exams

2022/2023

Uploaded on 11/02/2023

siham-hammou 🇹🇷

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Download old calculus III exam with solutions to help you master the course and understand it more. and more Exams Differential and Integral Calculus in PDF only on Docsity!

ISIK UNIVERSITY MATH2105 MIDTERM EXAM-2 29.12.2022 | Duration: 90 minutes | QI | | Q2) | Q3 | ] | Row No: | | Last Name: Firat Name: Student ID: | ‘T pledge my honor that I have not violated the} | . . ue Pignature: | honor code duriny this examination. Q1. (17 pts.) Find the local extreme values of the function f(z,y) = 2° + 4° — 6ay +2 if exists. 2 26 maahoy=o oye EF 1 ihe uit gle =o er Yel. then 40 of 2H? Oe 2 ree ows (9,2) and (2,2) oz 6 4 =6X, Ruy = Sy 7 fay B= Sex by Py = Bbxy- 36 = 3b (my-1) hoa At (0,0) Dlore) = 36(o-1) =-36<0.> a a sadolle pork at (0,0); anal He saclelie poimt is (o,0, 2). At (21, BAD= 34 (2-2-1) = 36-3 OF and $4 (2:2) = 6.2=)250. Thererfo ce. a dacat mininum vole ar (2,2) onl tHe. minimum volue i £(2,2) 2 8+8-24+2=—-%>