Use your finding(s) in part (2) to demonstrate that the simultaneous system of (3) nonlinear equations cos² (x + y) 1+ x2 2² – y? = 2 = (x – 2y + 3) sin(x – y), xy = has at least one solution.

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Use your finding(s) in part (2) to demonstrate that the simultaneous system of<br>(3)<br>nonlinear equations<br>cos² (x + y)<br>1+ x2<br>2² – y? = 2<br>= (x – 2y + 3) sin(x – y),<br>xy =<br>has at least one solution.<br>

Extracted text: Use your finding(s) in part (2) to demonstrate that the simultaneous system of (3) nonlinear equations cos² (x + y) 1+ x2 2² – y? = 2 = (x – 2y + 3) sin(x – y), xy = has at least one solution.
9. Consider the vector field v(x, y) = (x² – y², –2xy) over R2. (1) (0,0) is well defined. Explain why the index of v along any closed curve C not intersecting the origin (2) cases whether or not C encloses the origin separately). Compute the index of v along such a closed curve C (you must consider the two

9. Consider the vector field<br>v(x, y) = (x² – y², –2xy)<br>over R2.<br>(1)<br>(0,0) is well defined.<br>Explain why the index of v along any closed curve C not intersecting the origin<br>(2)<br>cases whether or not C encloses the origin separately).<br>Compute the index of v along such a closed curve C (you must consider the two<br>

Extracted text: 9. Consider the vector field v(x, y) = (x² – y², –2xy) over R2. (1) (0,0) is well defined. Explain why the index of v along any closed curve C not intersecting the origin (2) cases whether or not C encloses the origin separately). Compute the index of v along such a closed curve C (you must consider the two

Jun 03, 2022

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Use your finding(s) in part (2) to demonstrate that the simultaneous system of (3) nonlinear equations cos² (x + y) 1+ x2 2² – y? = 2 = (x – 2y + 3) sin(x – y), xy = has at least one solution.

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