# MAT301 Project

MAT301 Project #1 Due Saturday, February 27, 2021 The Basics Use Maple to solve all of the questions given below Question 1 Compute both an exact and a numerical value for each of the following numbers. a) b) c) d) 3 2 5 7 (23 − 3(117 − 48) ) / 7 − 5 ) 319π cos( ) 12 ln(2981) 83! 111! Question 2 Use the “Simplify” command on each of the following expressions a) 5 ln(2e ) b) 1 + cos(2x) Question 3 Factor each of these polynomials: 3 2 6x + 47x + 71x − 70 a) 6 5 4 3 12x − 56x +100x − 80x b) c) 2 + 20x + 8x − 4 Question 4 Input each of the following functions in Maple 2 g(x) = x ( f (x) = x(x − 2) , simplify each of the following: a) f (g(h(x ))) Question 5 Input f (x) = (1 + x the graphs of: – 3, b) h(g( f (x))) 2 ) −1 x + (x(x −1)) 3 − 4 x2 + x − 6 2 h(x) = x -1 ) and then compute and c) f (h(g( x))) into Maple. Then create a plot (over a) f (x), f (x −1), and f (x +1) b) f (x), f (2x), and f (8x) −3 ≤ x ≤ 3) containing Question 6 Using Maple, plot 1, if x < 0 f (x) = 1 − x 2 , if 0 ≤ x ≤ 2 x +1, if x > 2 Question 7 3 The equation x = x +1 has one real solution. Find its exact value with “SOLVE” command and its numerical value with the “FSOLVE” command. Verify this root by sketching the graph of the function generated from the equation given above. Question 8 An opened cylindrical can (opened on one end) has a volume of 100 cubic inches and a surface area of 100 square inches. Find the radius and the height of the can.

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