ull Ooredoo ?1:54 PM@ 27% ODone Screenshot 2021-01-15 at 10....8 of 32ssivity 1Let G be a rule that takes any real number greater than 4, then multiplies that numberby itself, then doubles the result and then subtracts 3. Express this rule mathematically,that is, if n represents the number, find G(n). Can you sketch this function, n on the X-vision) axis and G(n) on the Y-axis? What is the domain {D} and range {R} of G(n) ? List someelements in each set. What is the inverse function G-1(n)?ssWhat is the complete domain D and range R of the following multivariable functions:ivity 2a. w(x, y) = Vy – 4x2b. w(x,y) = xy-1)c. w = 2sin xy d. w = eye. w(x,y, z) =2x² + 4y²+6 z² f.w(x,y, z) = 7ty2+ z?ssQuestion 1 Describe and plot the graph of the function f(x, y) = 1– x- y in anivity 3xyz -orthogonal coordinate system?phtching) orthogonal axes, put in for some points, say (0,0,1) (0, 2,0) (1,0,0). You can freelyHint: This is the equation of a plane - no higher than linear terms appear, draw xyz –sketch a triangular portion of the plane z = f(x, y) by plotting the intersections with thecoordinate axes and joining them with line segments..Question 2 Plot a graph of the function g(r, t) = -/2r2 + 2t² it arises in the analysisof acoustic or signal phenomena in spatial dimension r and temporal dimension tWhat is the cone vertex?Hint: this is the equation of a circular cone z < 0, cone axis is the negative g- axis.Question 3 Describe and sketch the contour plot of z = f(x,y) = 4x² + y? using levelcurves of heights c = 0,1,2,3,4,5. To help you visualise, let x = 0, so that we have aparabola in the y, z -plane and then let y = 0 so we have a parabola in the x, z-plane.What is the parabola vertex? How is it orientated?

a. we have W(x,y)=y-4x2 we have to find the value of (x,y) where W(x,y) is defined y-4x2 is only…

What is the complete domain D and range R of the following multivariable functions: a. w(x, y) = Vy – 4x² b. w(x, y) = c. w = 2sin xy d. w = e x(у-1) 1 e. w(x, y, z) = /2x² + 4y² +6 z² f. w(x, y, z) = %3D x2+y2+ z?

What is the complete domain D and range R of the following multivariable functions: a. w(x, y) = Vy – 4x² b. w(x, y) = c. w = 2sin xy d. w = e x(у-1) 1 e. w(x, y, z) = /2x² + 4y² +6 z² f. w(x, y, z) = %3D x2+y2+ z?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

100%

ull Ooredoo ?
1:54 PM
@ 27% O
Done Screenshot 2021-01-15 at 10....
8 of 32
ss
ivity 1
Let G be a rule that takes any real number greater than 4, then multiplies that number
by itself, then doubles the result and then subtracts 3. Express this rule mathematically,
that is, if n represents the number, find G(n). Can you sketch this function, n on the X-
vision) axis and G(n) on the Y-axis? What is the domain {D} and range {R} of G(n) ? List some
elements in each set. What is the inverse function G-1(n)?
ss
What is the complete domain D and range R of the following multivariable functions:
ivity 2
a. w(x, y) = Vy – 4x2
b. w(x,y) = xy-1)
c. w = 2sin xy d. w = ey
e. w(x,y, z) =
2x² + 4y²+6 z² f.w(x,y, z) = 7ty2+ z?
ss
Question 1 Describe and plot the graph of the function f(x, y) = 1– x
- y in an
ivity 3
xyz -orthogonal coordinate system?
ph
tching) orthogonal axes, put in for some points, say (0,0,1) (0, 2,0) (1,0,0). You can freely
Hint: This is the equation of a plane - no higher than linear terms appear, draw xyz –
sketch a triangular portion of the plane z = f(x, y) by plotting the intersections with the
coordinate axes and joining them with line segments..
Question 2 Plot a graph of the function g(r, t) = -/2r2 + 2t² it arises in the analysis
of acoustic or signal phenomena in spatial dimension r and temporal dimension t
What is the cone vertex?
Hint: this is the equation of a circular cone z < 0, cone axis is the negative g- axis.
Question 3 Describe and sketch the contour plot of z = f(x,y) = 4x² + y? using level
curves of heights c = 0,1,2,3,4,5. To help you visualise, let x = 0, so that we have a
parabola in the y, z -plane and then let y = 0 so we have a parabola in the x, z-plane.
What is the parabola vertex? How is it orientated?

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