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Full Year Review MTH 251/252/253 – Calculus

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MTH251 – Differential Calculus Limits Continuity Derivatives Applications

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MTH251 – Differential Calculus Limits Evaluate limits at a point. Evaluate end behavior limits. Evaluate limits of quotients. L’Hôpitals Rule

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MTH251 – Differential Calculus Continuity Where does discontinuity occur? Jumps (piecewise functions) Asymptotes Holes Intervals where the function is undefined Given a graph or equation of a function; indicate where the function is discontinuous

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MTH251 – Differential Calculus Derivatives Polynomials Trigonometric and Inverse Trigonometric Exponential Logarithmic (esp. Natural Logs) Products Quotients Chain Rule

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MTH251 – Differential Calculus Applications Optimization Problems (i.e. max/min problems) Equations of tangent lines Rectangular Parametric

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MTH252 – Integral Calculus Indefinite Integrals Definite Integrals Methods of Integration Applications

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MTH252 – Integral Calculus Indefinite Integrals Antiderivative F(x) is an antiderivative of f(x) iff F’(x) = f(x) Indefinite Integral The set of all antiderivatives of a function.

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MTH252 – Integral Calculus Definite Integrals The limit of a Riemann Sum The Fundamental Theorem of Calculus

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MTH252 – Integral Calculus Methods of Integration Recognition: poly, trig, exp, log, … Algebraic Manipulation (Simple) Substitution Parts Powers of Trigonometric Functions Trigonometric Substitutions Partial Fractions

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MTH252 – Integral Calculus Applications Area Problems

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MTH253 – Analytic Geometry, Sequences, & Series Conics Polar Coordinates & Equations Sequences Series w/ Tests for Convergence Taylor & Maclaurin Series

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Conics Rotate (eliminate Bxy) Translate (eliminate Dx and Ey) … complete the squares Parabola Ellipse Circle Hyperbola Polar Forms Foci: Eccentricity: Directrixes: MTH253 – Analytic Geometry, Sequences, & Series

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Polar Coordinates & Equations Locate & Identify Points Graph Equations Circles, Flowers, Limaçons/Cardiods, Leminiscates, & Spirals Convert to and from Rectangular Coordinates & Equations Tangent Lines MTH253 – Analytic Geometry, Sequences, & Series

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Sequences An Ordered Set or List of Numbers Notation Given the first several terms, find the n th term. Evens 2n Odds 2n+1 or 2n-1 Alternating (–1) n or (–1) n+1 Constant Increment kn + a Factorials n! or (n + a)! or (n – a)! Convergence MTH253 – Analytic Geometry, Sequences, & Series

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Series The sum of the terms of a sequence. Notation Sequence of partial sums Test for Convergence Divergence Test Geometric Series & P-Series Integral Comparison & Limit Comparison Ratio & Root Alternating Series and Absolute Convergence MTH253 – Analytic Geometry, Sequences, & Series

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Taylor & Maclaurin Series Taylor Series at x = a Maclaurin Series Three Important Maclaurin Series MTH253 – Analytic Geometry, Sequences, & Series

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