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Calculus 2 practice final9/17/2023 The solutions to these sample finals are NOT available. Section 11. You should NOT assume that the final in your class will resemble any of the sample finals provided here. Office Hours: Monday, April 28 and Tuesday, April 29, 2:30-4:30 PM Exam. If you are a student, you may use these sample finals to gauge your preparation before taking a final exam. The sample tests are just to give you an idea of the a general idea of the topics covered, the level of difficulty, how questions may be worded and, if solutions are provided, what is the acceptable level of detail required in the. wish to work with others while doing the practice problems or preparing for an exam. Use the integral test to determine whether the following series converges or diverges.Disclaimer: These are actual final exams given in the past by various instructors at the Math Department. To view the Acrobat PDF files for each document, click on the symbol. Calculus II is being taught in two half-semester courses Math 226. Determine whether the following series converges absolutely, converges conditionally or diverges. Tabular Integration By Parts (not required, but useful) Arc Length. Determine whether the following series converges or diverges. Write a definite integral that represents the area inside the region enclosed by one loop DO NOTġ7. Give the coordinates of the points at which the curve crosses the axes. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Find the the interval of convergence of the power series ∞∑ġ6. Learn Calculus 2 in this full college course.This course was created by Dr. Write a definite integral that gives the volume of the solid of revolution formed by revolving the region bounded by y = x3 + x + 1, y = 1, and x = 1 about the line x = 2.ġ5. Write a definite integral that gives the volume of the solid of revolution formed by revolving the region bounded by the graph of x = e−yĪnd the y-axis between y=0 and y=1, about the x-axis.ġ4. Use a definite integral to express the length of the curve given by x = cos3 t, y = sin3 t, 0 ≤ t ≤ πġ3. Find the centroid of the region bounded by the curves y = x/2 and y = √ġ2. Write a definite integral that expresses the fluid force on the end of the tank when the oil is 4 feet deep?ġ1. The oil in the tank has a weight-density of 57 lb/ft3. Its height is 12 ft and width is 12 feet. A metal oil tank has cross-section that is a square rotated 45◦ as shown in the figure above. Express the volume of P as a definite integral. A solid figure P has R as a base region and cross-sections perpendicular to the x-axis are squares. Consider the region R bounded by y = 2x and y = x2. Integral does not converge, say so explicitly and show this.ĩ. (x + 1)1/3 + C to find the value of the following improper integrals, or, if an How much work does it take to pump the oil to the rim of the tank? Give your answer as a definite integral. The only things you are allowed to use when taking this exam are a pencil and an eraser. It is filled to within 2 feet of the top with olive oil weighing 57 lb/ft3. You will have 40 minutes to finish this exam. A conical tank (shown below) has a height of 12 feet and the diameter of the top is 16 feet. (a) If y(t) is the amount of salt in the tank after t minutes, write down the initial value problem describing the mixing process: (b) Find y(t), the amount of salt in the tank after t minutes.ħ. The mixture is kept uniform by stirring and flows out of the tank at the same rate of 5 gal/min. A brine containing 2 lb/gal of salt runs into the tank at the rate of 5 gal/min. A tank initially contains 100 gallons of brine in which 50 lb of salt are dissolved. FINAL EXAM CALCULUS 2 Name PRACTICE EXAM. Find a power series that represents the function 1Ħ. Find the slope of the line tangent to the parametric curve x = t cos t, y = 3t + t5 when t = 0.Ĥ. What can you say about the signs of a, b, c?ģ. The function f(x), whose graph is shown, has the Taylor polynomial of degree 2 about x = 0 given by P2(x) = a + bx + cx2. (c) y = x2 + x is a solution to y′ = 2(y − x2) + 1 (c) T FĪkx k converges at x=1 and x=2 then it converges at x = -2. Old exams could be found on the following link: Math 1242 Common Final Exams. (b) If bn > 0 and bn+1 < bn then the series To do well in the course, practice as many old common finals as possible. For each T/F question, write a careful and clear justification or describe a counterexample. If the statement is sometimes false, circle the printed capital F. For each part, if the statement is always true, circle the printed capital T. Practice Final Exam Math 1132 Spring 2009ġ.
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