Let O = {(x, y, z) = R³ | z > 0}, and let ¥ : O → R³ be the mapping defined as (x, y, z) = (x,x+y, x² + z²). (a) Show th

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Let O X Y Z R Z 0 And Let O R Be The Mapping Defined As X Y Z X X Y X Z A Show Th 1 (77.42 KiB) Viewed 40 times

Let O = {(x, y, z) = R³ | z > 0}, and let ¥ : O → R³ be the mapping defined as (x, y, z) = (x,x+y, x² + z²). (a) Show that is a smooth change of variables. (b) Let K = = {(x, y, z) | 0 ≤ x ≤ 4, −x ≤ y ≤ 4 − x, √25 – x² ≤ z ≤ √36 – x²} . y) z Use the change of variables theorem to evaluate the integrale dxdydz. [6] [9]