13. Find an equation for the tangent plane of the graph of f at the point (xo, yo, f(xo, yo)) for: (a) ƒ: R² → R, (x, y) → x − y + 2, (xo, yo) = (1, 1)

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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13. Find an equation for the tangent plane of the graph of f
at the point (xo, yo, f(xo, yo)) for:
(a) ƒ: R²2 → R, (x, y) ↔ x − y +2,
(xo, yo) = (1, 1)
(b)
(c)
ƒ: R² → R, (x, y) → x² + 4y²,
(xo, yo) = (2, -1)
f:
ƒ: R² → R, (x, y) → xy,
(xo, yo) =
(-1, −1)
(d) f(x, y) =
log (x + y) + x cos y + arctan(x + y),
(xo, yo) = (1, 0)
-2
(e) f(x, y) = √√√x² + y²,
(f) f(x, y) = xy,
(xo, yo)= (1, 1)
(xo, yo) = (2, 1)
Transcribed Image Text:13. Find an equation for the tangent plane of the graph of f at the point (xo, yo, f(xo, yo)) for: (a) ƒ: R²2 → R, (x, y) ↔ x − y +2, (xo, yo) = (1, 1) (b) (c) ƒ: R² → R, (x, y) → x² + 4y², (xo, yo) = (2, -1) f: ƒ: R² → R, (x, y) → xy, (xo, yo) = (-1, −1) (d) f(x, y) = log (x + y) + x cos y + arctan(x + y), (xo, yo) = (1, 0) -2 (e) f(x, y) = √√√x² + y², (f) f(x, y) = xy, (xo, yo)= (1, 1) (xo, yo) = (2, 1)
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