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Unformatted text preview: MATH 152 FALL 2009 CALCULUS II FOR THE MATHEMATICAL AND PHYSICAL SCIENCES WORKSHEET FOR MIDTERM II For a plain list of textbook sections covered, see the course syllabus on the website. Please email me if you encounter any errors or omissions. 1. IMPROPER INTEGRALS make sure it becomes a reflex to replace R by lim R R R integrating the finite integral R R may require any of the integration techniques covered in this course, including u- and trigonometric substitution, integration by parts or fractional parts B try [7.7 Pr31, Pr47] after youve integrated R R , you will need to evaluate the limit as R tends to infinity, which may require LHopitals rule or another argument B see examples above. in an analogous fashion, you want to be able to interpret and evaluate integrals in which one or both of the endpoints are points of discontinuity of the integrand B look at [7.7 Ex7] then try [7.7 Pr33] sometimes you may not be able to evaluate the integral precisely; however, if you are only re- quired to determine whether the integral converges or diverges, and it looks almost like some- thing you might be able to integrate, use the comparison test! B look at [7.7 Ex9, Ex10] then try [7.7 Pr59, Pr73] 2. ARC LENGTH, PARAMETRIC EQUATIONS AND POLAR COORDINATES memorize the formula for the arc length of a function y = f ( x ) B look at [8.1 Ex1] then try [8.1 Pr7, Pr10] practise drawing some parametric curves B look at [11.1 Ex6 and 7] then try [11.1 Pr34] know how to convert a parametric equation into a rectangular one, and conversely B look at [11.1 Ex1] then try [11.1 Pr11, Pr23] know formula for slope of the tangent to a parametric curve at a given point B look at [11.1 Ex8] then try [11.1 Pr47] WORKSHEET FOR MIDTERM II memorize arc length and speed formula for parametric curves B look at [11.2 Ex2 and Ex3] then try [11.2 Pr5, Pr21] know how to convert polar coordinates into rectangular ones, and conversely B look at [11.3 Ex2] then try [11.3 Pr3, Pr5]Ex2] then try [11....
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- Fall '08