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Unformatted text preview: Project 6 MAC 2311 1. Examine the piecewise-defined function below, and sketch the graph carefully on the axes: g ( x ) = e- x x < x = 0 2- 1 x < x < 1 1 x > 1 Evaluate the following limits: lim x - g ( x ) = lim x + g ( x ) = lim x 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 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? 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. Showfrom each corner and bending up the sides....
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