EXAMPLE 1.1The circumference of a circle (S) is approximated by the perimeters of inscribed and circumscribedn-sided polygons as shown in Figure 1.3. Prove the following:lim s" = s andlim Su) = S100

Approach: we will express the perimeter of polygons in terms of the radius of the circle R and the…

Answered: EXAMPLE 1.1 The circumference of a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. Find the circumference of the circle r= 4 cos 0 (Hint: the circle is complete for 0 to T).
O Question 10 Reina claims it is possible to approximate the area of a circle by cutting it into wedges and making a roughly quadrilateral shape with the wedges, as Length Do you support Reina's claim? If so, explain. If not, why not? A I support Reina because it is half the circumference,Tr, and is approximately equivalent to the sum of the arc lengths from half the wedges
1.
(B) Find the subsequent displacement for a simply supported beam of length (L) take a positive value for constant in the separation of variables method if the governing equation given by dzy +C?. dt2 d'y =0 where C EI/pA %D
s(2t)tat =? х* — 1 lim x-1 A) 2 B) C) D) -2 E) 0
(a) Let A, be the area of a polygon with n equal sides inscribed in a circle with radius r. By dividing the polygon into n congruent triangles with central angle 2n/n, show that the following is true. A, = n? sin(2 kle
(b) (0 State the type of triangle shown above. (ii) Determine the value of angle PNM (ii) Calculate the area of the triangle MVP. A sequence of figures is made up of stars, using dots and sticks of different lengths. The first in the sequence are shown below. Figure 1 Figure 2 Figure 3 Study the pattern of numbers in each row of the table below. Each row relates to a figure in the sequence of figures started above. Some rows have not been included in the table. (a) Complete Rows (i), (ii) and (iii) Figure Number of Sticks (S) Number of Dots (D) 1 12 13 2 24 25 3 36 37 4 48 49 (i) 5 (ii) 11 (iii) The sum of the number of dots three pairs of consecutive figur 156 ares are recorded. This information for the first le below. Figure 1 and Figure 2 Figure 2 and Figure 3 Figure 3 and Figure 4 13 + 25 = 38 25-37-62 37+49 86 Determine the TOTAL number of dots in (i) Figure 7 and Figure & (ii) Figure n and Figure (n+1)1

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EXAMPLE 1.1 The circumference of a cirdle (S) is approximated by the perimeters of inscribed and circumscribed n-sided polygons as shown in Figure 1.3. Prove the following: lim S = s and lim Su) = S %3D n-00 n00