Unformatted text preview: t = 0 and g ′ ( t ) = ∂f ∂x ( x + t △ x,y + △ y ) △ x. (b) Show that we can write f ( x,y + △ y ) − f ( x,y ) = ∂f ∂y ( x,y + δ 2 ) △ y where | δ 2 | ≤ |△ y | . 7. (a) Use Proposition 3.3.7 to prove Equation ( 3.11 ). (b) Use Defnition 3.3.3 to prove Equation ( 3.11 ) directly. 8. Show that iF f ( x,y ) and g ( x,y ) are both di²erentiable real-valued Functions oF two variables, then so is their product h ( x,y ) = f ( x,y ) g ( x,y ) and the Following Leibniz Formula holds: −→ ∇ h = f −→ ∇ g + g −→ ∇ f....
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- Fall '08
- Calculus, Expression, Gottfried Leibniz, following directions, point starts