Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 12.8, Problem 26PS
To determine
To graph :
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.Define f: R- R by f(x) = rx + d, where r and d are real constants. Show that for f to be linear, it
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4r1-2
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I2
X122+3
Justify your answer:
3. Find the image of d and preimage of if the transformation is given as
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4.
Use the given transformation to evaluate the integral , (4x + 8y) dA where R is the parallelogram with vertices
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Chapter 12 Solutions
Calculus
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- 6) What transformation do you apply to get to figure A?* O KY) - (y. x) O (K y) - (x y) O K) - (2x. 2y) Oy)-(0.5x, 0 5y) O Ky) - (xy) O K) - (xy)arrow_forward5B. Evaluate √x+y (y-x)² dxdy using the transformation x+y=u,y-x = v. 1/03arrow_forwardSuppose ABCD from the diagram below was reflected across the line x = 3 then reflected across the line x = 10 to become A"B"C"D". What single transformation would result in the same image?arrow_forward
- 6. Graph the reflection of ADEF through both the x-axis and the y-axis, where D (9, 10), E (8,-2), and F (1,4). 7. Determine the transformation given the preimage AABC where A (1, 0), B (6, -7), and C (0,-4) and the image AA'B'C' where A' (0, -1), B' (-7,-6), and c'(-4, 0).arrow_forwardProblem 12 (Answer the following three questions) Let T : R² → R² be a transformation given by T : (u, v) → (x, y), where x = u + v and y = v³. The region R in xy-plane is given by -y ≤x≤1-y, 0≤y ≤ 2. Let S be the corresponding region in uv-plane given by a ≤ u ≤ b, c ≤ v ≤ d. Find a, b,c, d. Ans: 0, 1, 0, 2 Problem 13 Compute the Jacobian of T i.e., det JȚ. Problem 14 Using the change of variable formula find ſſ ƒ(x, y)dA = ſ[¸ ƒ(x(u,v), y(u, v))| det Jr] du dv R SS₁ 1 R 3y²/3 dA. Ans: 3² Ans: 2arrow_forward3. Suppose is fixed and T: R² → R² is the transformation that rotates R² by radians. Find T(1,0) and T(0,1)arrow_forward
- A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes as shown in the figure below. (Enter your answers as a comma-separated list of equations.) R is bounded by y = 2x − 2, y = 2x + 2, y = 2 − x, y = 4 − xarrow_forward7. Consider the transformation T(x, y) = (y,x(1+y²)). Draw the image of the picture here under T. Hint: Parameterize each of the 5 line segments and proceed as in 3(d). To speed things, divide up the task. Check your answer with the instructor.arrow_forward16. If H is a subgraph of G, then show that dg(u,v) < dn(u, v).arrow_forward
- 38. a. Consider a linear transformation T from R³ to R. What are the possible values of dim(ker T)? Explain. b. Consider a linear transformation T from R4 to R'. What are the possible values of dim(imT)? Explain.arrow_forward5. Use the transformation u = x + y, v = x - y to find – y)e=²-y² (x dA. - R Where R is the rectangular region enclosed by the lines x +y = 0,x + y = 1, x – y = 1, x – y = 4.arrow_forward1. Use the transformation x= 2u +3v, y=3u-2v to evaluate (x+y)dA, where R is the %3D R square with vertices at A(0, 0), B(2,3), C(3, - 2) and D(5, 1). Graph the region R in the xy-plane, as well as the region in the uy- plane it is mapped into. Show all your work in an organized and understandable manner.arrow_forward
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