![]() Find the radius and the interval of convergence of a power series.Recognize if the power series centered at the origin or at another number.Outcome 7: Upon completion of this course, the student will have a working knowledge of power series. Use the ratio and root tests to determine the absolute convergence of infinite series.Use the alternating series test (Leibniz test) to determine convergence or divergence.Use the p-series to determine convergence or divergence.Use the integral test and comparison tests for convergence or divergence of infinite series.Recognize geometric series and determine convergence or divergence.Outcome 6: Upon completion of this course, the student will be able to determine convergence or divergence of infinite series. Recognize bounded and unbounded sequences.Use the squeeze theorem for convergent or divergent sequences.Outcome 5: Upon completion of this course, the student will be able to determine the convergence or divergence of sequences. ![]() ![]() Evaluate an improper integrals with a discontinuous integrand, as well as one with an unbounded domain.Recognize if an improper integral is convergent or divergent.Outcome 4: Upon completion of this course, the student will be able to evaluate improper integrals. Evaluate the integrals for powers of trigonometric functions.Evaluate integrals by utilizing partial fractions.Evaluate integrals using integration by parts and the tabular method.Use the trigonometric formulas from memory.Evaluate integrals using trigonometric substitution.Outcome 3: Upon completion of this course, the student will be able to evaluate integrals using trigonometric substitution, integration by parts, partial fractions, and by the integral tables. Use formulas to find the surface area of solids at revolution.Determine the arc length by using the arc length formula.Outcome 2: Upon completion of this course, the student will be able to determine the arc length and the surface area of solids of revolution. Calculate the volumes of solids of revolution using the cylindrical shells method.Calculate the volumes of solids of revolution using circular discs and washers.Outcome 1: Upon completion of this course, the student will be able to determine the volumes of solids of revolution. ![]() Michigan Transfer Network (MiTransfer) - Utilize this website to easily search how your credits transfer to colleges and universities. MATH 1770 is part of the sequence of courses required for most engineering, science, and mathematics majors and includes volumes of solids of revolution improper integrals sequences and series Taylor series Maclaurin series differentiation and integration of power series and calculus with parametric and polar curves. Prerequisites: MATH 1760 with grade C or better or an equivalent college course or an acceptable score on a placement or prerequisite exam Suppose that a curve C is described by the parametric equations x=f(t), y=g(t), $$$ $$$.MATH 1770 - Analytic Geometry & Calculus 2 We are going to define the length of a general curve by first approximating it by a polygon and then taking a limit as the number of segments of the polygon is increased. We use the same approach as with areas and volumes. However, in general it can be very diffcult to find length of some curve. (We can use the distance formula to find the distance between the endpoints of each segment.) If the curve is a polygon, we can easily find its length we just add the lengths of the line segments that form the polygon.
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