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Algebra
Pregunta

A metal plate is situated in the \( x y \) -plane ...

A metal plate is situated in the \( x y \) -plane and occupies the rectangle \( 0 \leq x \leq 10,0 \leq y \leq 8 \) , where \( x \) and \( y \) are measured in meters. The temperature at the point \( ( x , y ) \) in the plate is \( T ( x , y ) \) . where \( T \) is measured in degrees Celsius. Temperatures at equally spaced points were measured and recorded in the table. 

(a) Estimate the values of the partial derivatives \( T _ { x } ( 6,4 ) \) and \( T _ { v } ( 6,4 ) \) . What are the units? 

(b) Estimate the value of \( D _ { u } T ( 6,4 ) \) , where \( u = ( i + j ) / \sqrt { 2 } \) . Interpret your result. 

(c) Estimate the value of \( T _ { x p } ( 6,4 )\) 

Answer

\(\left. \begin{array} { l } { \text { 11. (a) } \approx 3.5 ^ { \circ } C / m , - 3.0 ^ { \circ } C / m } \\ { \text { (b) } \approx 0.35 ^ { \circ } C / m \text { by Equation } 14.6 .9 \text { (Definition } 14.6 .2 \text { gives } } \\ { \approx 1.1 ^ { \circ } C / m . ) } \\ { \text { (c) } - 0.25 } \end{array} \right.\)

Solución
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