# Full Year Review MTH 251/252/253 – Calculus. MTH251 – Differential Calculus Limits Continuity Derivatives Applications.

## Presentation on theme: "Full Year Review MTH 251/252/253 – Calculus. MTH251 – Differential Calculus Limits Continuity Derivatives Applications."— Presentation transcript:

Full Year Review MTH 251/252/253 – Calculus

MTH251 – Differential Calculus Limits Continuity Derivatives Applications

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

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

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

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

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

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.

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

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

MTH252 – Integral Calculus Applications Area Problems

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

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

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

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

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

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

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