[T] Lamé ovals (or superellipses) are plane curves of equations ( x a ) n + ( y b ) n = 1 where a , b, and n are positive real numbers. a. Use a CAS to graph the regions R bounded by Lamé ovals for a = 1. b =2, n =4 and n=6. respectively. b. Find the transformations that map the region R bounded by the Lamé oval x 4 + y 4 = 1, also called a squircle and graphed in the following figure, into the unit disk. c. Use a CAS to find an approximation of the area A ( R ) of the region R x 4 + y 4 = 1 . Round your answer to two decimal places.
[T] Lamé ovals (or superellipses) are plane curves of equations ( x a ) n + ( y b ) n = 1 where a , b, and n are positive real numbers. a. Use a CAS to graph the regions R bounded by Lamé ovals for a = 1. b =2, n =4 and n=6. respectively. b. Find the transformations that map the region R bounded by the Lamé oval x 4 + y 4 = 1, also called a squircle and graphed in the following figure, into the unit disk. c. Use a CAS to find an approximation of the area A ( R ) of the region R x 4 + y 4 = 1 . Round your answer to two decimal places.
[T] Lamé ovals (or superellipses) are plane curves of equations
(
x
a
)
n
+
(
y
b
)
n
=
1
where a, b, and n are positive real numbers.
a. Use a CAS to graph the regions R bounded by Lamé ovals for a= 1.b=2,n=4 and n=6.
respectively.
b. Find the transformations that map the region R bounded by the Lamé oval x4+y4= 1, also called a squircle and graphed in the following figure, into the unit disk.
c. Use a CAS to find an approximation of the area A(R) of the region R
x
4
+
y
4
=
1
. Round your answer to two decimal places.
Find the area of the surface formed by revolving the graph of f(x) = x3 on the interval [0, 1] about the x-axis, as shown in Figure
Let f(x) = 2x - 1 and g(x) = x - 3 on [ 3 , 6 ]. Find the center of gravity of the region between the graphs of f and g.
Find, to two decimal places, the x-coordinate of the centroid of the region in the first quadrant bounded by the x-axis, the curve y = tan-1 x, and the line x = √3.
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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