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2. Decide if the integral: S e compute it. The formula: So converges or diverges. Should the integral converge do = arcsin + C may be helpful.

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Keith Leannon
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15 Jan 2018
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1. A table leg has height 100 cm. At a height of y cm above the ground it has has circular cross sections with radius r = sin y + 2 cm. (a) Draw a picture of the table leg. (b) Show that the volume of a horizontal slice (sin” y + 4 sin y + 4)Ay. (c) Compute the integral flº (sin”y + 4 sin y + 4)dy. Use your answer to deduce the volume of the table leg. The formula / sin" rdt = -sin"-1 x COS X + " sin"-2 rdr, n positive may be helpful.

(8) Consider the sequence an given by 2 4 6 8 10 12 67:80:101... Given that the pattern shown continues, find the limit lim On. (Hint: Find an explicit formula for an before deciding what the limit is.) n00 (A) O (B) 1 (C) 2 (D) The sequence is increasing, so it diverges. (E) None of the above.

Modeling Your company is going to make its own boxes!
It has been decided the box should hold 0.45m3 (0.45 cubic meters which are equal to 45 liters) of nuts

and bolts.

The box should have a square base, and double thickness bottom.

Cardboard costs $0.47 per square meter.

It is up to you to decide the most economical shape and size. (Except that the base must be square.)

You must show how you have developed a model to decide the most economical size. In this assignment, it is suggested that you follow the following steps

(a)  Draw a sketch of your box and a sketch of a net from which your box can be constructed.

(b)  Make a formula for the volume and surface area of your box

(c)  Develop a formula for the cost of the box using the area and volume

(d)  Draw a graph of the cost of the box using the y-axis as the cost and x-axis as the width of the base.

Remember to include enough information to show us how you drew your graph. Include either the points you plotted or the formula and drawing package used if you found the graph electronically.

(e)  Use the graph to determine the minimum cost, width, and height of the box

(f)  What are your recommendations for the shape and dimensions of the box?

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