Question

Draw a contour map of the function f(x, y) = y/(2x 2 + y 2 ) showing several level curves.

Answer #1

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Draw a contour map for the surface f(x,y)=16-x^2-y^2 using the
contour lines C= 0, 4,7 and 16

draw a contour plot for h(x,y)=2x^2-y-2.
show work.

A contour map is shown for a function f on the square
R = [0, 2] ⨯ [0, 2].
(a) Use the Midpoint Rule with m = n = 2 to
estimate the value of
f(x,y) dA.
R
(Round your answer to the nearest integer.)
(b) Estimate the average value of f. (Round your answer to
one decimal place.)

sketch a contour diagram for the function f(x,y)=x-y^2 with at
least four labeled contours

4. Consider the function z = f(x, y) = x^(2) + 4y^(2)
(a) Describe the contour corresponding to z = 1.
(b) Write down the equation of the curve obtained as the
intersection of the graph of z and the plane x = 1.
(c) Write down the equation of the curve obtained as the
intersection of the graph of z and the plane y = 1.
(d) Write down the point of intersection of the curves in (b)
and...

Examine the function f(x, y) = 2x 2 + 2xy + y 2 + 2x − 3 for
relative extrema.
Use the Second Partials Test to determine whether there is a
relative maximum, relative minimum, a saddle point, or insufficient
information to determine the nature of the function f(x, y) at the
critical point (x0, y0), such that fxx(x0, y0) = −3, fyy(x0, y0) =
−8, fxy(x0, y0) = 2.

make a contour map with x=0, y=0, z=0, z=1, z=2, and z=4 for
z=x^2+y^2 then sketch the graph

a) Find a parametric equation for a curve given as an
intersection of a sphere x^2 + y^2 + z^2 = 1 and a plane x + z = 1,
where 0 ≤ a ≤ 1.
b) Do the contour plot of the function f(x, y) = x 2 −y 2 . The
contour plot is a collection of several level curves drawn on the
same picture (be sure to include level curves for positive,
negative and zero value of...

Write a MATLAB code to plot a contour graph of f(x, y) = x^2 +
y^2 for −2 ≤ x ≤ 2 and −3 ≤ y ≤ 3. Use the interval of 0.1 in the
grid.

consider the 2 variable function f(x,y) = 4 - x^2 - y^2 - 2x -
2y + xy
a.) find the x,y location of all critical points of f(x,y)
b.) classify each of the critical points found in part a.)

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