/ 2 100% + 2 CALCULUS I, SPRING 2023 MATH 1210-090 INSTRUCTOR: WILL FELDMAN Problem 3....

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/ 2 100% + 2 CALCULUS I, SPRING 2023 MATH 1210-090 INSTRUCTOR: WILL FELDMAN Problem 3. Consider the function 3x 2 0x 1 f(x) = {1 1 x 2 3-x 2x 3. sketch the graph of on the interval x E [0,3] and use that to help evaluate the definite integral +3 f(x)dx. Problem 4 (Optional: bonus credit 3 pts). At 6pm a driver enters a toll road with a speed limit of 80 miles per hour. On entrance they receive a slip which is stamped with the entry location and time. At 6:45pm they exit through a toll booth 70 miles away and return their slip to pay the toll. Prove that the driver, at some point during that 45 minutes, was going at least 10 miles per hour over the speed limit and should receive a speeding ticket! 100% + 1/2 Name: uID: Problem 1. Find the following anti-derivatives: (a) / 26 x- cos(3x) + x1/4 dx 3x (b) | 2 + 23 dx Problem 2. A toy rocket launches off of the top of a 10 meter tall platform at time t = 0. The initial velocity of the rocket is 0 m/s and the acceleration is given by the following function of time a(t) = 3t+4 m/s for 0 / 2 100% + 2 CALCULUS I, SPRING 2023 MATH 1210-090 INSTRUCTOR: WILL FELDMAN Problem 3. Consider the function 3x 2 0x 1 f(x) = {1 1 x 2 3-x 2x 3. sketch the graph of on the interval x E [0,3] and use that to help evaluate the definite integral +3 f(x)dx. Problem 4 (Optional: bonus credit 3 pts). At 6pm a driver enters a toll road with a speed limit of 80 miles per hour. On entrance they receive a slip which is stamped with the entry location and time. At 6:45pm they exit through a toll booth 70 miles away and return their slip to pay the toll. Prove that the driver, at some point during that 45 minutes, was going at least 10 miles per hour over the speed limit and should receive a speeding ticket! 100% + 1/2 Name: uID: Problem 1. Find the following anti-derivatives: (a) / 26 x- cos(3x) + x1/4 dx 3x (b) | 2 + 23 dx Problem 2. A toy rocket launches off of the top of a 10 meter tall platform at time t = 0. The initial velocity of the rocket is 0 m/s and the acceleration is given by the following function of time a(t) = 3t+4 m/s for 0