For each function in Exercises 1–4, evaluate (a) f ( 0 , 0 ) ; (b) f ( 1 , 0 ) ; (c) f ( 0 , − 1 ) ; (d) f ( a , 2 ) ; (e) f ( y , x ) ; and (f) f ( x + h , y + k ) ; [Hint: See Quick Examples 1–3. ] f ( x , y ) = x 2 − y − x y + 1
For each function in Exercises 1–4, evaluate (a) f ( 0 , 0 ) ; (b) f ( 1 , 0 ) ; (c) f ( 0 , − 1 ) ; (d) f ( a , 2 ) ; (e) f ( y , x ) ; and (f) f ( x + h , y + k ) ; [Hint: See Quick Examples 1–3. ] f ( x , y ) = x 2 − y − x y + 1
Solution Summary: The author calculates the value of the function f(x,y)=x2-y-xy+1 for the point.
1. Given the vector field F(x, y, z) = -zi, verify the relation
1
VF(0,0,0) lim
+0+ volume inside S
ff F• Nds
S.
where S, is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
Let a = (-4, 5, 4) and 6 = (1,0, -1).
Find the angle between the vector
1) The exact angle is cos
2) The approximation in radians is
Chapter 8 Solutions
Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th
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