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. Let f: R²R where f(x, y) = √√√1-x² - y² and c = (0, -2). (a) Find and simplify Df(c). (b) Find and simplify f(c) + L((x, y) — c). (c) What is the equation of the tangent plane to the graph of z = √1-2² - y² through the point (0, -, f(c))?

. Let f: R²R where f(x, y) = √√√1-x² - y² and c = (0, -2). (a) Find and simplify Df(c). (b) Find and simplify f(c) + L((x, y) — c). (c) What is the equation of the tangent plane to the graph of z = √1-2² - y² through the point (0, -, f(c))?

Advanced Engineering Mathematics
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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Real Analysis II Please solve problems in few lines as given sample
2. Let ƒ: R² → R where f(x, y) = √1 - x² - y² and c = (0,-2). (a) Find and simplify Df(c). (b) Find and simplify f(c)+L((x, y) — c). - (c) What is the equation of the tangent plane to the graph of z = √1 - x² - y² through the point (0, -2, f(c))?
Transcribed Image Text:2. Let ƒ: R² → R where f(x, y) = √1 - x² - y² and c = (0,-2). (a) Find and simplify Df(c). (b) Find and simplify f(c)+L((x, y) — c). - (c) What is the equation of the tangent plane to the graph of z = √1 - x² - y² through the point (0, -2, f(c))?
10:41 ← Expert Answer Ⓒ Step1 a) ⇒ Step2 b) (a) af dx (c) af ay =) = (b) f(c) + L ((x, y) = c) and Hence, f (x, y) = = => z = D f(c) = (cat)) ale) 2x g= 2 y əg ax =) 93 az 8+ (4,4) (x-2, 4-2) 8 + 4(x-2) + 4 (5-2). 2 x² + y² -1 equation of = a ) x² + y2 x² + y²_z = 0 a = 4 af ax at 10 = 4x + 4y-2 = 8 ? = (4,4) (2² +2²)+L((x,y)-(2,23) 8 + L ((x-2, y-2)) 23 25 = 23 ay C = (2,2) = 4 f(c) = 8 tangent plane 4 (x-2) + + (y-2) -1 (2-8) = 0 ag => - 3x1.- ax IS 29 dy √x = 4 Equation of this plane (x-) +33 (5-2) -1 (2-0) = 0 8
Transcribed Image Text:10:41 ← Expert Answer Ⓒ Step1 a) ⇒ Step2 b) (a) af dx (c) af ay =) = (b) f(c) + L ((x, y) = c) and Hence, f (x, y) = = => z = D f(c) = (cat)) ale) 2x g= 2 y əg ax =) 93 az 8+ (4,4) (x-2, 4-2) 8 + 4(x-2) + 4 (5-2). 2 x² + y² -1 equation of = a ) x² + y2 x² + y²_z = 0 a = 4 af ax at 10 = 4x + 4y-2 = 8 ? = (4,4) (2² +2²)+L((x,y)-(2,23) 8 + L ((x-2, y-2)) 23 25 = 23 ay C = (2,2) = 4 f(c) = 8 tangent plane 4 (x-2) + + (y-2) -1 (2-8) = 0 ag => - 3x1.- ax IS 29 dy √x = 4 Equation of this plane (x-) +33 (5-2) -1 (2-0) = 0 8
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