Question 3. The equation2.x + y? + z? + 2.xy – 2x – 2y – 6z +1= 0implicitly defines a function z =z(x, y) satisfying z > 3.(a)Express and as functions of x, y, z.(b)Verify that z(2, –2) = 5. Use the linearization to estimate z(2.1, –2.1).Find all critical points of z(x, y). Using the second derivative test, characterize each criticalpoint as a local maximum, local minimum or a saddle point.(Hint: you will need to calculate the second order derivatives , , at each critical point. Tosimplify the expression, keep in mind that and are both 0 at critical points.)82 z(d)Find the maximum of z(x, y) along the line 2x +y = 5. (You don't need to prove that thesolutions you find truly give the maximum.)

Partial differentiation is a branch of differential equations. When a function has more than one…

Question 3. The equation 2x + y? +z? + 2.xy – 2x – 2y – 6z +1 = 0 implicitly defines a function z = z(x, y) satisfying z > 3. (a) Express and as functions of x, y, z. (b) Verify that z(2, –2) = 5. Use the linearization to estimate z(2.1, -2.1).

Question 3. The equation 2x + y? +z? + 2.xy – 2x – 2y – 6z +1 = 0 implicitly defines a function z = z(x, y) satisfying z > 3. (a) Express and as functions of x, y, z. (b) Verify that z(2, –2) = 5. Use the linearization to estimate z(2.1, -2.1).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

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