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Students: You will be expected to have the following formulas memorized for the rst exam, and for the remainder of the course Consider this document fair warn-ing If any of the integrals are standalone problems, you must show all your work If any of the integrals are embedded within a larger problem, you can use the in-tegrals without showing work
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Important Note We will focus on the new material covered in Chapter 2 However, the precalculus material from sections 1 1-1 3 is fair game for the exam It would be a good idea to review WebAssign, written homework, and class activities and bring any questions you have to o ce hours or class on Monday This review is meant to supplement, not replace, the review sheet handed out on Monday Be
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Math 2300 { Calculus II { University of Colorado Final exam review problems 1 A slope eld for the di erential equation y0 = y e x is shown Sketch the graphs of the solutions that satisfy the given initial conditions Make sure to label each sketched graph
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A spherical snowball melts in such a way that the instant at which its radius is 20 cm, its radius is decreasing at 3 cm min At what rate is the volume of the ball of snow changing at that instant? Diagram: Draw a picture of the melting snowball Label the variables of interest
- Math 1300: Calculus I Fall 2020 Lecture: Section 4. 1: Related Rates
1 3 Oil is spilling out of a tanker in a circular pattern whose radius is increasing at a rate of 3 ft sec How fast is the area increasing when the radius is 60ft? Example 1 4 (Due to Dr Patrick Newberry) A 10 ft ladder is leaning against a building If the bot-tom is pulled away from the building at a rate of 2 ft sec, at what rate is the top of the ladder falling when the bottom is 6 ft
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Omar ies his kite 150m high, where the wind causes it to move horizontally away from him at the rate of 5m per second In order to maintain the kite at a height of 150m, Omar must allow more string to be let out At what rate is the string being let out when the length of the string already out is 250m?
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- Borel Functional Calculus and some applications.
Then, I'll talk a little bit about the continuous Functional Calculus and nally introduce the Borel Functional Calculus as an extension of this last one If time allows, I'll give a couple of interesting applications
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