Evaluate the expression n=2. 8(n + 1) = ___
2 answers:
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Answer:
A.
B.
Step-by-step explanation:
A. At first, it´s useful to move everything to one side and name it as a function f(x,y,z):
:
To proceed to find the tangent plane at (1+π,1,1), we use the following equation for the tangent plane:
Where (x₀,y₀,z₀) is the specified point where we want the tangent plane to connect. Now we need to find the gradient vector of f:
Now we differentiate f with respect to x,y and z to find those coordinates:
We are ready to use the equation for the tangent plane
The tangent plane has an equation , and the orthogonal vector to this plane is one made of the coefficients of the plane, a normal vector for this plane is (-1,2,1).
To find a normal line to this surface in (1+π,1,1) we find a normal line to the plane, and because we know that (-1,2,1) is a normal vector, then the line has to have the same direction, so we normalize that vector to get the direction:
And because that line has to pass through (1+π,1,1) we conclude the vector equation for this line is the following:
and from this equation: