[T] The Sierpinski triangle is obtained from a triangle by deleting the middle fourth as indicated in the first step, by deleting the middle fourths of the remaining three congruent triangles in the second step, and in general deleting the middle fourths of the remaining triangles in each successive step. Assuming that the original triangle is shown in the figure, find the areas of the remaining parts of the original triangle after N steps and find the total length of all of the boundary triangles after N steps.
[T] The Sierpinski triangle is obtained from a triangle by deleting the middle fourth as indicated in the first step, by deleting the middle fourths of the remaining three congruent triangles in the second step, and in general deleting the middle fourths of the remaining triangles in each successive step. Assuming that the original triangle is shown in the figure, find the areas of the remaining parts of the original triangle after N steps and find the total length of all of the boundary triangles after N steps.
[T] The Sierpinski triangle is obtained from a triangle by deleting the middle fourth as indicated in the first step, by deleting the middle fourths of the remaining three congruent triangles in the second step, and in general deleting the middle fourths of the remaining triangles in each successive step. Assuming that the original triangle is shown in the figure, find the areas of the remaining parts of the original triangle after N steps and find the total length of all of the boundary triangles after N steps.
For the region under
f(x) = 4x2
on
[0, 4],
show that the sum of the areas of the upper approximating rectangle approaches
256
3
,
that is
lim n→∞ Rn =
256
3
.
Compute algebraically the resultant of the following complanar displacements: 100 N at 30°, 141.4 N at 45°, and 100 N at 240°. Check your result graphically.
Show that the area between the curve y = 1/x and the x-axisfrom x = 10 to x = 20 is the same as the area between thecurve and the x-axis from x = 1 to x = 2. Show that the area between the curve y = 1>x and the x-axis from ka to kb is the same as the area between the curve and the x-axis from x = a to x = b (0 < a < b, k > 0).
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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