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

Solutions

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

Next > < Previous

Related Solutions

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

given the 3rd order differential equation: y''' - 3y'' + 2y' = ex / (1 + e-x) i) set u = y' to reduce the order of the equation to order 2 ii) solve the reduced equation using variation of parameters iii) find the solution of the original differential equation

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

Consider the differential equation y '' − 2y ' + 10y = 0; ex cos(3x), ex sin(3x), (−∞, ∞). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(ex cos(3x), ex sin(3x)) = _____ANSWER HERE______ ≠ 0 for −∞ < x < ∞. Form the general solution. y = ____ANSWER HERE_____

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

Consider the function given as example in lecture: f(x, y) = (e x cos(y), ex sin(y)) (6.2) Denote a = (0, π/3) and b = f(a). Let f −1 be a continuous inverse of f defined in a neighborhood of b. Find an explicit formula for f −1 and compute Df−1 (b). Compare this with the derivative formula given by the Inverse Function Theorem.

Solve y’’ – 11y’ + 24y = ex +3x using reduction of order

Answer the following using Binomial theorem and Pascal's Triangle: a. Find the middle term in the...

Answer the following using Binomial theorem and Pascal's Triangle: a. Find the middle term in the expansion of (4x – x3)14 b. Use Pascal’s triangle to expand (3x + 2y)6.

Solve for the unknown x and y in the following nonlinear equation using Taylor’s theorem (Use...

Solve for the unknown x and y in the following nonlinear equation using Taylor’s theorem (Use ?0 = 5 and ?0 = 5 for initial approximations) ?^2? − 3?^2 = 75 ?^2 − ? = 19

solve y'' + 4y =6 sin (t);y(0) =6, y'(0)=0 using 1st laplace transforms, 2nd undertinend coefficent,...

solve y'' + 4y =6 sin (t);y(0) =6, y'(0)=0 using 1st laplace transforms, 2nd undertinend coefficent, and 3rd variation of parameters.

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

Solve the following initial value problem using the undetermined coefficient technique: y'' - 4y = sin(x), y(0) = 4, y'(0) = 3

Write a program (fortran 90) that calls a subroutine to approximate the derivative of y=sin(x)+2x^2 using...

Write a program (fortran 90) that calls a subroutine to approximate the derivative of y=sin(x)+2x^2 using a one-sided difference approach fx = (fi-fi-1)/deltaX and a centered difference approach fx = (fi+1-fi-1)/deltaX. The value of the function f and its derivative fx should be evaluated at x=3.75. Your code should print both values tot he screen when it runs.

Write a script le using conditional statements to evaluate the following function, assuming that the scalar variable x has a value. The function is Y = ex+1 fo

Write a script le using conditional statements to evaluate the following function, assuming that the scalar variable x has a value. The function isY = ex+1 for x < -1, y = 2 + cos(πx) for -1 ≤ x ≤ 5, and y = 10(x - 5) + 1 for x ≥ 5. Use your le to evaluate y for x = -5, x = 3, and x = 15, and check the results by hand.

Subjects