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Differentiate....then evaluate both at 1,2,3 see if that helps
find all critical points of
f(x, y)=e^x(1-cos y)
and classify these critical points.
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Two surfaces are said to be orthogonal at a point P if the normals to their tangent planes are perpendicular at P. Show that the surfaces z= 1/2(x²+y² -1) and z=1/2(1- x²-y²) are orthogonal at all points of intersection.
Let f = f(u,v) and u = x + y, v = x - y
i) assume f to be twice differentiable and compute f_{xx} and f_{yy} in terms of f_{u}, f_{v}, f_{uu}, f_{uv} and f_{vv}.
ii)express the wave equation:
((∂²f)/(∂x²))-((∂²f)/(∂y²))=0
in terms of partial derivatives of f with respect to u and v.
The first answer was the right way of doing it. im not sure about thia local quadraticisation
Two surfaces are said to be tangential at a point P if they have the same tangent plane at P . Show that the surfaces z = √(2x²+2y²-1) and z = (1/3)√(x²+y²+4) are tangential at the point (1, 2, 3).
find the local linearization of the function f(x,y) = √(x³+y4) at the point (1,2). use it to estimate f(1.04,1.98).
An unevenly heated plate has temperature T(x,y) in degrees celcius at the point (x,y). If T(2,1)=135, and Tx(2,1)=16 and Ty(2,1)= -15, estimate the temperature at the point (2.04, 0.97).
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