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Let F(T) be the cost of heating your house, in dollars per day, when the average outside temperature is T Celsius degrees. (a) Make a rough sketch a possible graph of F(T). (There are many possible...

a) Sketch a function that has a positive first derivative for x < −5, a derivative of zero for −5 < x < 5 and a negative first derivative for x > 5. (b) Call this function f(x). On the...

I want to find ∂_x(u)(0,1) i.e. u_x where u(x,t) is the solution of the heat equation ∂_t(u) = ∂_x^2(u) i.e. u_t = u_(xx) with the initial condition u(x,0) = X_[0,∞](x) = 0 when x<=0 and = 1 when...

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