Consider the following nonlinear equation, x - 2xy + y = 19. (i) Check that the...

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Consider the following nonlinear equation, x³ - 2xy + y² = 19. (i) Check that the point (3, 4) is on the curve defined by the equation. (ii) Calculate the slope of the curve at (3,4). (hint: use the implicit function theorem) (iii) Suppose x increases to x = 3.01, estimate how much change occurs to y accordingly. And compare your estimate with true value that you can obtain using a computer. Consider the following nonlinear equation, x³ - 2xy + y² = 19. (i) Check that the point (3, 4) is on the curve defined by the equation. (ii) Calculate the slope of the curve at (3,4). (hint: use the implicit function theorem) (iii) Suppose x increases to x = 3.01, estimate how much change occurs to y accordingly. And compare your estimate with true value that you can obtain using a computer.