# P06 - Project 6 MAC 2311 1 Examine the piecewise-dened...

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Project 6 MAC 2311 1. Examine the piecewise-defined function below, and sketch the graph carefully on the axes: g ( x ) = e - x x < 0 0 x = 0 2 - 1 x 0 < x < 1 1 x > 1 Evaluate the following limits: lim x 0 - g ( x ) = lim x 0 + g ( x ) = lim x 0 g ( x ) = lim x 1 - g ( x ) = lim x 1 + g ( x ) = lim x 1 g ( x ) = Although we have not discussed this yet, test your intuition and understanding of limits and limit notation by guessing the value of the following limits: lim x →∞ g ( x ) = lim x →-∞ g ( x ) = 2. Sketch the function h ( x ) = x 2 - 6 x + 5 x - 5 . (Consider simplifying first.) What continuous function is identical to h ( x ) for all x except x = 5 ? Evaluate the limit: lim x 5 h ( x ) . What type of discontinuity does this function have?

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3. A rectangular piece of cardboard of dimensions 8 by 17 inches is used to make an open-top box by cutting out a small square of side x from each corner and bending up the sides. Show that the volume of the box is V ( x ) = x (8 - 2 x )(17 - 2 x )
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