expand ex sin y using the maclaurins theorem up to 3rd term degree

expand e^x sin y using the maclaurins theorem up to 3^rd term degree

Expert Solution

the Maclaurin expansion of any two-variable function is given by the formula shown above. To determine the first-degree Taylor polynomial linear approximation, we first compute the partial derivative f_x(x,y) and f_y(x,y). we Then evaluate these partials and the function itself at the point (0,0).

To determine the second-degree Taylor polynomial (quadratic) approximation, we need to evaluate the send partial derivatives of the function and evaluate the derivatives at point(0,0) this can be clearly seen in the image below: $Q (x, y) "> Q (x, y we need the second partials of the function f$

$(0, 0) "> (0$

the expansion of e^x sin y using the Maclaurin theorem up to the 3^rd term therefore becomes:

joseph irungu answered 2 years ago

given the 3rd order differential equation: y''' - 3y'' + 2y' = ex / (1 +...

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Consider the differential equation y '' − 2y ' + 10y = 0; ex cos(3x), ex sin(3x),...

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Consider the function given as example in lecture: f(x, y) = (e x cos(y), ex sin(y))...

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Solve the following initial value problem using the undetermined coefficient technique: y'' - 4y = sin(x),...

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