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1. Find gradient for the function (x, y, z) = log (x² + y² + z²) at the point (1, 2, 1).

1. Find gradient for the function (x, y, z) = log (x² + y² + z²) at the point (1, 2, 1).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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Please see the image and answer all questions detailly, clearly, and without mistakes. please help me, don't blindly copy from internet please, i need true help only. thanks

1. Find gradient for the function 4(x, y, z) = log (x² + y² + z²) at the point (1, 2, 1). 2. Find the directional derivative of y(x, y, z) = x²yz + 4x z² at the point (1, −2, −1) in the direction of the vector 2i +j+ 2k. 3. Find a, b and c if (x + y + az)i + (bx + 2y − z)j + (−x + cy + 2z)k is irrotational. 4. Evaluate the line integral ſ [(3x² + 6y)dx − 14yz dy + 20xz dz] along the curve C parameterized by r(t) = t i + t² j + t³ k whose ending vertices are (0, 0, 0) and (1, 1, 1). 5. Using Green's theorem evaluate √ [(x² + y²)dx − 14xy dy], where C is the closed curve of the region bounded by y² = x and x² = y.
Transcribed Image Text:1. Find gradient for the function 4(x, y, z) = log (x² + y² + z²) at the point (1, 2, 1). 2. Find the directional derivative of y(x, y, z) = x²yz + 4x z² at the point (1, −2, −1) in the direction of the vector 2i +j+ 2k. 3. Find a, b and c if (x + y + az)i + (bx + 2y − z)j + (−x + cy + 2z)k is irrotational. 4. Evaluate the line integral ſ [(3x² + 6y)dx − 14yz dy + 20xz dz] along the curve C parameterized by r(t) = t i + t² j + t³ k whose ending vertices are (0, 0, 0) and (1, 1, 1). 5. Using Green's theorem evaluate √ [(x² + y²)dx − 14xy dy], where C is the closed curve of the region bounded by y² = x and x² = y.
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