Sketch a graph of the function y = x^3e^−x showing clearly where it is concave up or concave down. Indicate the x-coordinates of any maxima, minima and points of inflection and find the asymptotic behaviour. Show all your reasoning.

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Q: (4) Let x € (0, 1). Use induction to prove that 1 - In X for all natural numbers n ≥ 2.

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Q: 1) Solve the following ODE using the power series method

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Q: 9. Consider the graph G defined as follows: G has exactly 6 vertices, labelled by the integers 1, 2,…

A: This is a question from the graph theory.

Q: (c) The curves f(x, y) = x³+y-1 g(x, y) = y³r+1 intersect near the point (₁,3₁). Using the point…

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