Problem 3: Consider the surface defined by the equation
z = ln(5x<sup>2</sup> + y + 3).
a) Use MATLAB and the surf() function to plot the plane over the interval x ∈ [-2,2],
y ∈ [-2, 2]. Choose an appropriate view to best visualize the plane and label axes
appropriately.
Solution:
%code
b) Find an equation for a tangent plane to the surface at the point P = (1, 1).
Solution:
Put your math/explanation here...
c) Use MATLAB to replicate your plot from part (a) but now also plot the tangent surface
computed in part (b). Also, use the plot3() function to plot the point where the tangent
plane was computed at. Set the view so it's clear the tangent plane is indeed tangent to
the surface at the given point.
Solution:
%code
