If f(x, y) = 2x² + 5y² and u is the unit vector in the direction of T 6 which of the following expressions equals Duf(x, y)

Elementary Linear Algebra (MindTap Course List)
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Chapter5: Inner Product Spaces
Section5.1: Length And Dot Product In R^n
Problem 17E: Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of...
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If
f(x, y) = 2x² + 5₁²
and
u
is the unit vector in the direction of
π
6
which of the following expressions equals
Du f(x, y)
?
lim
h→0
lim
h→0
lim
h→0
2
²(x + = ₁ ) ² + 5 ( x + √2/²₁ ) ² − (2x² + 58² )
2x
5y
-
h
None of the given choices
lim
h→0
2
2
2 ( x + √2/²₁) ²³ + 5(x + √2/² » ) ² − (2x² + 53²)
-
y
-
h
2
2 ( x + √/³√n ) ² + 5(x + ²√n) ² -
+ 5 (y +_h) − (2x² + 5y²)
h
2
2
² ( x − — ^)² + 5 ( x − 4 /³^₁) ³² - (2x² + 55²)
√3
2
y
h
Transcribed Image Text:If f(x, y) = 2x² + 5₁² and u is the unit vector in the direction of π 6 which of the following expressions equals Du f(x, y) ? lim h→0 lim h→0 lim h→0 2 ²(x + = ₁ ) ² + 5 ( x + √2/²₁ ) ² − (2x² + 58² ) 2x 5y - h None of the given choices lim h→0 2 2 2 ( x + √2/²₁) ²³ + 5(x + √2/² » ) ² − (2x² + 53²) - y - h 2 2 ( x + √/³√n ) ² + 5(x + ²√n) ² - + 5 (y +_h) − (2x² + 5y²) h 2 2 ² ( x − — ^)² + 5 ( x − 4 /³^₁) ³² - (2x² + 55²) √3 2 y h
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