(a) Check the local linearity of f(x, y) = ex sin ynear x = 1, y = 2 by making a table
Chapter 14, Problem 19(choose chapter or problem)
(a) Check the local linearity of f(x, y) = ex sin ynear x = 1, y = 2 by making a table of values off for x = 0.9, 1.0, 1.1 and y = 1.9, 2.0, 2.1.Express values of f with 4 digits after the decimalpoint. Then make a table of values for x =0.99, 1.00, 1.01 and y = 1.99, 2.00. 2.01, againshowing 4 digits after the decimal point. Do both tableslook nearly linear? Does the second table lookmore linear than the first?(b) Give the local linearization of f(x, y) = ex sin yat (1, 2), first using your tables, and second usingthe fact that fx(x, y) = ex sin y and fy(x, y) =ex cos y.
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