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# HNRS CALCULUS II MATH 2214

A-State

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This 3 page Class Notes was uploaded by Ubaldo Larkin on Friday October 2, 2015. The Class Notes belongs to MATH 2214 at Arkansas State University taught by Suzanne Melescue in Fall. Since its upload, it has received 24 views. For similar materials see /class/217706/math-2214-arkansas-state-university in Mathematics (M) at Arkansas State University.

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Date Created: 10/02/15

Calculus II Review for Exam 3 Section 78 0 Evaluate improper integrals with an infinite limit of integration 0 Evaluate improper integrals with unbounded integrands 0 Use L Hopital s rule to evaluate limits if needed Section 81 o Memorize the arc length formula to find the length of a curve Section 82 0 Find the area ofa surface of revolution 1 will give the basic surface area formula S J27 r f Section 83 I Calculate the center of mass in a onedimensional or two dimensional system I Find the centroid of a region bounded by given curves 1 will give Formulas 9 on page 546 Section 111 I Write out terms of a given sequence I Write a formula for the general term of a sequence I Determine if a sequence is convergent or divergent I Determine if a sequence is bounded above bounded below both that is bounded or neither I Determine if a sequence is increasing decreasing or neither Section 112 I Write out terms of a sequence of partial sums I Determine if a telescoping series converges or diverges and find the sum of each convergent series Remember that you may first have to change the form of the an using partial fraction decomposition before examining the sum I Determine if a geometric series converges or diverges and find the sum of each convergent geometric series Apply the divergence test to show divergence Remember that the divergence test does not show convergence Section 113 I Determine if a pseries converges or diverges I Determine convergence or divergence using the integral test Remember to verify the hypotheses ie positive continuous and decreasing function before applying the test Section 114 I Determine convergence or divergence of an infinite series using the direct comparison test Determine convergence or divergence an infinite series using the limit comparison I Rem ember to 1 write the series that you are using as a comparison state whether it converges or diverges 2 make the comparison using an inequality or a limit 7 depending on which test you decide to use 3 and then write the conclusion Section 115 I Determine convergence or divergence of an alternating series I Possible approach to the problems First find nlgnm an If the limit is not zero then the series diverges by the divergence test If the limit is zero then proceed with the alternating convergence test Section 116 Determine absolute convergence conditional convergence or divergence of an infinite series Remember that in the case of conditional convergence you may need to use a convergence test from Sections 112 7 114 Determine convergence or divergence an infinite series using the ratio test This test is useful for infinite series involving 391 l r or 11 u w PmIbidthonlmso llodm 391 g I Determine convergence or divergence of an infinite series using the root test Calculus II Review for Exam 1 The following is a list of the sections and topics that may appear on the rst exam To determine what you need to review in more detail work through homework assignments without the aid of notes Study and then rework those problems that caused difficulties Perhaps writing and taking a practice exam will help overcome the anxiety associated with test taking Section 53 0 Evaluate derivatives of integral functions using the Fundamental Theorem of Calculus Part 1 0 Evaluate de nite integrals using the Fundamental Theorem of Calculus Part 2 Section 54 0 Know the basic integration formulas Remember the C in every answer Section 55 0 Evaluate indefinite and definite integrals using usubstitution Notice the form of the answer for each type Tips Pick u as the inside of the messiest part Don t forget du Never write the integral with x s and u 5 together Remember to change limits if needed Section 61 Find the area between two curves using either horizontal rectangles or vertical rectangles 0 Vertical rectangles Area top function bottom functiondx 0 Horizontal rectangles Area right function left functiondy Section 62 Find the volume of a solid of revolution using the disldwasher method 0 Disk Method Volume If radius2 thickness 0 Washer Method Volume If outer radius2 inner radius2 thickness 0 Remember that thickness of vertical rectangles is dx and the thickness of horizontal rectangles is dy 0 Remember to choose values for the upper and lower limits that match the variable Find the volume of a solid using known cross sections with areaA o Perpendicular to the xaxis Volume IAx dx 0 Perpendicular to the yaxis Volume IA y dy Section 63 Find the volume of a solid of revolution using the shell method 0 Volume 27rradius height thickness 0 Remember that thickness of vertical rectangles is dx and the thickness of horizontal rectangles is dy 0 Remember to choose values for the upper and lower limits that match the variable

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