Question

Given?(?,?)= 9− ?^2

a). State the function’s domain and range.

b). Sketch the surface in 3-D. Be sure to clearly label your axes and label any points on the surface that cross an axis.

c). On a separate graph from part (b), sketch the following level curves in the domain of the function: f(x, y) = 0, f(x, y) = 5, and f(x, y) = 9. Label the value of f(x, y) on each level curve.

Answer #1

a) The function has the domain of all real values for the inpput x, and the range is 0 ≤ z ≤ 9

b) The curve is a parabolic cylinder, that is inerted along Z axis when seen from XY plane. A graphing calculator can show below sketch.

It cuts the X axis at ±3 and crosses the Z axis at z = 9

c) All level curves are straight lines on the XY plane , perpendicular to th X axis.

f(x, y) = 0 is the set of lines x = ±3, z = 0

f(x, y) = 5 is the set of lines x = ±2, z = 5

f(x, y) = 9 is the line x = 0, z = 9

Given ?(?,?) = sqrt(x + y)
a). What’s the domain and range of f(x, y)?
b). Sketch any 3 level curves in the domain of the function (on
the same graph). Label any points where the level curves cross an
axis AND label the value of f(x, y) on each curve.
c. Please do the same for g(x,y)= -y/x^2

a) Find the domain and range of the following function:
f(x,y)=sin(ln(x+y))
b) sketch the domain.
c) on seperate graph, sketch three level curves

For f(x,y)=ln(x^2−y+3). -> Find the domain
and the range of the function z=f(x,y).
-> Sketch the domain, then
separately sketch three distinct level curves.
-> Find the linearization of
f(x,y) at the point
(x,y)=(4,18).
-> Use this linearization to determine the
approximate value of the function at the point (3.7,17.7).

1) Use traces to sketch and identify the surface:
(?/3)^2+(?/5)^2+(?/9)^2=1
2) Find and sketch domain of the function
?(?,?)=√(?^2+?^2−9)
3) Sketch the graph of the function:
?(?,?)=5?^2+3?^2

Find traits and sketch the graph the equation
for a function g ( x ) that shifts the function f ( x ) = x + 4 x 2
− 16 two units right. Label and scale your
axes.
Domain:
x – Intercepts:
y – Intercept:
Vertical Asymptotes:
Holes:
End Behavior:
Range:

(16 marks total) Using the IS-LM model discussed in chapter 10,
suppose you’re given the following information: • The consumption
function is given by C = 40 + 0.5 (Y − T). • The investment
function is given by I = 150 − 10r. • T = 120, and G = 170. (a) Find planned expenditure P E as a function of Y and r. (b)
For the case where r = 8, find the value of Y that
produces...

Consider the surface defined by z = f(x,y) = x+y^2+1.
a）Sketch axes that cover the region -2<=x<=2 and
-2<=y<=2.On the axes , draw and clearly label the contours
for the eights z=0 ,z=1,and z=2.
b)evaluate the gradients of f(x,y) at the point (x,y) = (0.-1),
and draw the gradient vector on the contour diagrqam .
c)compute the directional derivative at(x,y) = (0,-1) in the
direction V =<2,1>.

f(x)=x/(x^2)-9
Use the "Guidelines for sketching a curve A-H"
A.) Domain
B.) Intercepts
C.) Symmetry
D.) Asymptotes
E.) Intervals of increase or decrease
F.) Local Maximum and Minimum Values
G.) Concavity and Points of Inflection
H.) Sketch the Curve

Sketch the graph of a function f(x) that satisfies all of the
conditions listed below. Be sure to clearly label the axes.
f(x) is continuous and differentiable on its entire domain,
which is (−5,∞)
limx→-5^+ f(x)=∞
limx→∞f(x)=0limx→∞f(x)=0
f(−2)=−4,f′(−2)=0f(−2)=−4,f′(−2)=0
f′′(x)>0f″(x)>0 for −5<x<1−5<x<1
f′′(x)<0f″(x)<0 for x>1x>1

11) Let p(x) = (4x^2-9)/(4x^2-25)
(a) What is the domain of the function p(x)?
(b) Find all x- and y-intercepts.
(c) Is function p(x) an even or odd function?
(d) Find all asymptotes.
(e) Find all open intervals on which p is increasing or
decreasing.
(f) Find all critical number(s) and classify them into local
max. or local min..
(g) Sketch the graph of p. [Please clearly indicate all the
information that you have found in (a)–(f) above.]

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