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    Multivariable Calculus Problems Pertaining to a Bell Surface

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    We have the function f(x,y) = e^(-x^2 + y^2) :
    a. To draw some level curves;
    b. Calculate the gradient and determine the stationary points;
    c. To write the equation of the tangent plane to z = f(x,y) in the point (0, 0, f(0, 0)), and in the point A (1,1,f(1,1));
    d. To write the Taylor formula of f(x,y) stopped to the 2nd order, with center in the point (1,1);
    e. Tell if the surface cross the tangent plane in A.

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    Solution Summary

    We solve several problems in mulitivariable calculus pertaining to a bell-shaped surface.