[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.
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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