## Topic outline

### Limits & Continuity

• ZA Solving limits with substitution Page
• How to solve LIMITS BY FACTORING Page
• CONJUGATE METHOD for solving limits Page
• Use limit laws to evaluate limits of combination functions Page
• How to find limits on CRAZY GRAPHS Page
• Limits at infinity Page
• Infinite limits Page
• Limits of trig functions: Everything you need to know! Page
• How to find the ONE-SIDED LIMITS of a function Page
• How to prove that the limit does not exist Page
• The precise definition of the limit EXPLAINED! Page
• Finding delta from a graph and the epsilon-delta definition of the limit Page
• How to find the limit using SQUEEZE THEOREM Page
• Limit of an inequality, with squeeze theorem Page
Restricted Not available unless: Your Department is not empty
• Finding the domain by investigating continuity Page
• How to make a function continuous (for a piecewise function) Page
• How to find REMOVABLE DISCONTINUITIES Page
• How to use the Intermediate Value Theorem Page
• Intermediate value theorem to prove a root in an interval Page
• Prove the equation has at least one real root Page
• Limits of composite functions - How to find them? Page
• Jump discontinuities - What are they? Page

### Derivatives

• How to calculate the difference quotient Page
• DEFINITION OF THE DERIVATIVE to find the derivative Page
• Power rule for derivatives Page
• PRODUCT RULE for derivatives Page
• Product rule - 3+ functions Page
• Quotient rule Page
• Reciprocal rule Page
• Chain rule combined with power rule Page
• Chain rule for derivatives, with product rule Page
• Chain rule for derivatives, with quotient rule Page
• Chain rule for derivatives, with trig functions Page
• Derivatives of TRIG FUNCTIONS Page
• Derivative of cot^4(x/2) Page
• Derivatives of inverse trig functions - arcsin Page
• Derivatives of inverse trig functions - arccot Page
• Derivatives of HYPERBOLIC functions Page
• Derivatives of inverse hyperbolic functions Page
• Implicit differentiation COMPLETELY EXPLAINED! Page
• Finding the derivative of a function with e^x Page
• Derivatives of logarithms Page
• How to use LOGARITHMIC DIFFERENTIATION to find the derivative Page
• Derivative of x^x Page
• EQUATION OF THE TANGENT LINE Page
• Value that makes two tangent lines parallel Page
• DIFFERENTIABILITY and horizontal and vertical tangent lines Page
• Equation of the normal line at a point Page
• Average rate of change of a function Page
• Finding HALF LIFE Page
• Continuous compounding interest Page

### Applications of Derivatives

• ESTIMATE THE ROOT with linear approximation Page
• Linearization of a function at a point Page
• Optimization - Calculus Page
• How to find CRITICAL POINTS Page
• Where is the function INCREASING AND DECREASING? Page
• INFLECTION POINTS and CONCAVITY Page
• FIRST DERIVATIVE TEST to find the max and min Page
• How to use the SECOND DERIVATIVE TEST Page
• How to find VERTICAL ASYMPTOTES!! Page
• How to find HORIZONTAL ASYMPTOTES Page
• How to find SLANT ASYMPTOTES Page
• All about GRAPH SKETCHING!! Page
• Maxima and minima on a CLOSED interval Page
• Dimensions that maximize the area of the rectangle Page
• OPTIMIZATION: Dimensions that maximize the volume of a cylinder Page
• OPTIMIZATION: Dimensions of a rectangle that minimize its perimeter Page
• OPTIMIZATION: Dimensions that maximize the volume of a box Page
• Dimensions of the rectangle with largest area inscribed in an equilateral triangle Page
• Largest area of a rectangle inscribed in a semicircle Page
• Points on the cone closest to a point Page
• Max volume of a rectangular box inscribed in a sphere Page
• Maximum volume of a cone shaped cup Page
• Largest possible volume of a cylinder inscribed in a sphere Page
• Dimensions that minimize the surface area of a cylinder Page
• OPTIMIZATION: Dimensions that minimize page size with a given printed area
• OPTIMIZATION: Dimensions that minimize the surface area of an open top box Page
• OPEN-TOP BOX?!! How to find the smallest possible surface area Page
• OPTIMIZATION: Point on the line closest to another point Page
• Minimizing the product of two real numbers Page
• Finding numbers with the smallest sum of squares Page
• OPTIMIZATION: Production level, sale price that maximize profit Page
• OPTIMIZATION: Sales level that maximizes revenue Page
• OPTIMIZATION: Time when velocity is minimum Page
• Related Rates Page
• RELATED RATES: Radius of the balloon Page
• RELATED RATES: Ladder sliding down the wall Page
• RELATED RATES: Distance between the person and the plane Page
• RELATED RATES: Water level in the tank Page
• RELATED RATES: Price of the product Page
• MEAN VALUE THEOREM (MVT) for derivatives Page
• How to use ROLLE'S THEOREM Page
• How to use NEWTON'S METHOD Page
• How to use L'HOSPITAL'S RULE Page
• POSITION FUNCTION Page
• All about a PARTICLE'S POSITION function Page
• Instantaneous velocity Page
• HOW HIGH CAN YOU THROW THE BALL?!! How fast is it going when it hits the ground? Page
• Dropping a coin from the roof (VERTICAL MOTION!) Page
• How to find MARGINAL COST, REVENUE AND PROFIT Page

### Integrals

• Summation Notation - Finding the Sum Page
• How to find a Riemann sum using LEFT ENDPOINTS Page
• Riemann sums with right endpoints Page
• THE MOST ACCURATE WAY TO DO A RIEMANN SUM Page
• Close only counts in horseshoes, hand grenades, and Riemann sums Page
• Trapezoidal Rule Page
• Simpson's Approximation Page
• Definite Integral Page
• ARE YOU FINDING THE RIGHT AREA?!! Area under vs. area enclosed by a graph Page
• Definite integral of an even function Page
• Definite integral of an odd function Page
• PART 1 OF THE FUNDAMENTAL THEOREM OF CALCULUS! Page
• PART 2 OF THE FUNDAMENTAL THEOREM OF CALCULUS! Page
• Net change theorem Page
• Indefinite Integrals Page
• Properties of integrals Page
• Find f(x) given f''(x), its second derivative Page
• Find f(x) given f'''(x), its third derivative Page
• Initial Value Problem Page
• Find f given f'' and initial conditions Page
• Solving Integrals Page
• U-Substitution Page
• U-Substitution in Definite Integrals Page
• Integration by Parts Page
• Integration by parts two times Page
• Integration by parts three times Page
• U-substitution with integration by parts Page
• Integration by parts to prove the reduction formula Page
• A TOTALLY DIFFERENT WAY to do integration by parts! Page
• Partial fractions, distinct linear factors Page
• Partial fractions, distinct linear factors, example 2, part 1 of 2 Page
• Partial fractions, distinct linear factors, example 2, part 2 of 2 Page
• Partial fractions, distinct linear factors, example 3 Page
• Partial fractions, repeated linear factors Page
• Using partial fractions with DISTINCT QUADRATIC FACTORS Page
• Partial fractions, distinct quadratic factors, example 2 Page
• Partial fractions, distinct quadratic factors, example 3 Page
• Partial fractions, repeated quadratic factors Page
• Partial fractions, rationalizing substitution Page
• Integrating with partial fractions: how to factor difficult denominators Page
• Partial fractions, two ways to find the constants Page
• Integrating a trig function using u-substitution! Page
• Trigonometric integrals - sin^mcos^n, odd m Page
• Trigonometric integrals - sin^mcos^n, odd n Page
• Trigonometric integrals - sin^mcos^n, m and n even Page
• Integrals of trigonometric functions, tan^msec^n, odd m Page
• Integrals of trigonometric functions, tan^msec^n, even n Page
• Integrals of trigonometric functions, sin(mx)cos(nx) Page
• Integrals of trigonometric functions, sin(mx)sin(nx) Page
• Integrals of trigonometric functions, cos(mx)cos(nx) Page
• Hyperbolic integrals... pretty much just like trig integrals Page
• Integrals of Inverse Hyperbolic Functions Page
• How to solve EVERY trigonometric substitution problem ever! Page
• Trigonometric substitution with secant Page
• Trigonometric substitution with sine Page
• Trigonometric substitution with tangent Page
• Integral of a quadratic function Page
• Improper integrals, case 2 Page
• Improper integrals, case 3 Page
• Improper integrals, case 5 Page
• COMPARISON THEOREM WILL FINALLY MAKE SENSE! Page
• Integrals using reduction formulas Page
• How to use inverse hyperbolic functions to evaluate integrals Page
• Partial fractions are SPECIAL! Page
• PARTIAL FRACTIONS example with distinct linear factors Page
• Trig substitution - How to solve? Page

### Applications of Integration

• Average Value of a Function Example 1 Page
• Area between curves - dx Page
• Area between curves - dy Page
• Area between curves - sketching Page
• Arc Length Page
• Arc length x=g(y) Page
• Arc length - simpson's rule Page
• Surface Area of Revolution Page
• Surface area of revolution - simpson's rule Page
• Surface of Revolution Page
• Volume of rotation: disk method about the y-axis or x-axis Page
• Volume of rotation: disk method about the y-axis or x-axis Page
• Volume of rotation: disk method about the x-axis or y-axis Page
• Volume of rotation: washer method about the x-axis or y-axis Page
• Volume of rotation: washer method about y-axis or x-axis Page
• Volume of rotation: washer method about x-axis or y-axis Page
• Volume of rotation: cylindrical shells about the y-axis or x-axis Page
• Volume of rotation: cylindrical shells about the x-axis or y-axis Page
• Mean value theorem for integrals Page
• Work done using a rope to lift a weight Page
• Work Done on Elastic Springs Page
• Work Done by a Variable Force Page
• Moments of the system Page
• Moments of the system, x-axis Page
• Center of mass of the system Page
• Center of mass of the system, x-axis Page
• Hydrostatic pressure Page
• Hydrostatic force Page
• Vertical Motion (integration) Page
• Rectilinear Motion Page
• Centroids of Plane Regions Page
• Centroid of the plane - simpson's rule Page
• Area of the triangle with the given vertices Page
• Present and Future Value Page
• Present and Future Value Example 2 Page
• Present and Future Value Example 3 Page
• Present and Future Value Example 4 Page
• Present and Future Value Example 5 Page
• Consumer and Producer Surplus Page