In the following exercises, the function T : S → R , T ( u , v ) = ( x , y ) on the region S = { ( u , v ) | 0 ≤ u ≤ 1 , 0 ≤ v ≤ 1 } bounded by the unit square is given, where R ⊂ R 2 is the image of S under a. Justify that the function T is a C transformation. b. Find the images of the vertices of the unit square S through the function T. c. Determine the image R of the unit square S and graph it. 359. x = 2 u − v , y = u + 2 v
In the following exercises, the function T : S → R , T ( u , v ) = ( x , y ) on the region S = { ( u , v ) | 0 ≤ u ≤ 1 , 0 ≤ v ≤ 1 } bounded by the unit square is given, where R ⊂ R 2 is the image of S under a. Justify that the function T is a C transformation. b. Find the images of the vertices of the unit square S through the function T. c. Determine the image R of the unit square S and graph it. 359. x = 2 u − v , y = u + 2 v
Find the image of the semi-infinite strip x ≥ 0, 0 ≤ y ≤ π under the transformation w = exp z, and label corresponding portions of the boundaries.
Assume that x,y € R and z=x+iy € C. Calculate the part a) using the given countour and assuming that ?→∞. For part b), use variable transformation of z=e3ix.
Let f(x) = 21 - x2 and g(x) = x2 + 3. Use symmetry, if appropriate, to help find the center of gravity, ( x, y ), of the bounded region enclosed by the graphs of f and g.
Finite Mathematics & Its Applications (12th Edition)
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY