CALCULUS SINGLE VAR W/ACCESS >CI<
CALCULUS SINGLE VAR W/ACCESS >CI<
8th Edition
ISBN: 9781305764583
Author: Stewart
Publisher: CENGAGE C
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Chapter E, Problem 41E

Evaluate each telescoping sum.

  1. (a) i = 1 n [ i 4 ( i 1 ) 4 ]
  2. (b) i = 1 100 ( 5 i 5 i 1 )
  3. (c) i = 3 99 ( 1 i 1 i + 1 )
  4. (d) i = 1 n ( a i a i 1 )
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The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 1. Select all that apply: ☐ f(x) is not continuous at x = 1 because it is not defined at x = 1. ☐ f(x) is not continuous at x = 1 because lim f(x) does not exist. x+1 ☐ f(x) is not continuous at x = 1 because lim f(x) ‡ f(1). x+→1 ☐ f(x) is continuous at x = 1.
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A homeware company has been approached to manufacture a cake tin in the shape of a "ghost" from the Pac-Man video game to celebrate the 45th Anniversary of the games launch. The base of the cake tin has a characteristic dimension / and is illustrated in Figure 1 below, you should assume the top and bottom of the shape can be represented by semi-circles. The vertical sides of the cake tin have a height of h. As the company's resident mathematician, you need to find the values of r and h that minimise the internal surface area of the cake tin given that the volume of the tin is Vfixed- 2r Figure 1 - Plan view of the "ghost" cake tin base. (a) Show that the Volume (V) of the cake tin as a function of r and his 2(+1)²h V = 2
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