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13 Nov 2019
(5 points) Consider the curves in the first quadrant that have equations y Aexp(3x), where A is a positive constant. Different values of A give different curves. The curves form a family, F. Let P (8,5). Let C be the member of the family F that goes through P. A. Let y- f(x) be the equation of C. Find f(x B. Find the slope at P of the tangent to C slope = 6 C. A curve D is perpendicular to C at P. What is the slope of the tangent to D at the point P? slope- D. Give a formula g(y) for the slope at (x, y) of the member of F that goes through (x, y). The formula should not involve A or z. E. A curve which at each of its points is perpendicular to the member of the family F that goes through that point is called an orthogonal trajectory to F. Each orthogonal trajectory to F satisfies the differential equation dxg() where g(y) is the answer to part D Find a function h(y) such that -h(y) is the equation of the orthogonal trajectory to F h(y) - (43/2)-(3/2)y2 that passes through the point P
(5 points) Consider the curves in the first quadrant that have equations y Aexp(3x), where A is a positive constant. Different values of A give different curves. The curves form a family, F. Let P (8,5). Let C be the member of the family F that goes through P. A. Let y- f(x) be the equation of C. Find f(x B. Find the slope at P of the tangent to C slope = 6 C. A curve D is perpendicular to C at P. What is the slope of the tangent to D at the point P? slope- D. Give a formula g(y) for the slope at (x, y) of the member of F that goes through (x, y). The formula should not involve A or z. E. A curve which at each of its points is perpendicular to the member of the family F that goes through that point is called an orthogonal trajectory to F. Each orthogonal trajectory to F satisfies the differential equation dxg() where g(y) is the answer to part D Find a function h(y) such that -h(y) is the equation of the orthogonal trajectory to F h(y) - (43/2)-(3/2)y2 that passes through the point P
Nestor RutherfordLv2
23 Aug 2019