organize the following into 2 categories: derivatives & integrals slope of a tangent line slope...
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Where Have We Been Calc AB Break Down 1)Limits 2)Derivatives 3)Applications of Derivatives 4)Integrals 5)Application of IntegralsTRANSCRIPT
Organize the following into 2 categories: DERIVATIVES & INTEGRALS
Slope of a Tangent LineSlope of a Curve
Instantaneous Rate of Change
Find where a function is increasing
Find where a function is concave down
Find an inflection point
Find a critical point
Finding a maximum of a function
Finding a Rate of Change
Chain Rule
Product RuleGiven a Rate, Find a TotalArea under a curve
Area between Curves
Volume of a Solid
U-Substitution
Given Acceleration, Find Distance
Given Velocity, Find Displacement
Riemann Sums
Anti-Derivative
Calculus BC Unit 1 Day 1
Little ReviewWhere have we beenWhere are we going
Where Have We Been
Calc AB Break Down1) Limits2) Derivatives3) Applications of Derivatives4) Integrals5) Application of Integrals
Limits Graphically
Limits Algebraically
Methods:1) Plug in2) Factor3) Getting Sneaky (Multiplying by “1”)4) Some you just have to remember
Big Point of Limits: Continuity
Derivatives!!! Ready?!?!Names:Slope of a Tangent LineSlope of the CurveInstantaneous Rate of Change
Examples of Derivatives we’ve Learned
What the Derivatives tells us!
Applications of Derivatives
1) Equation of Tangent Line2) Equation of Normal Line (perpendicular)3) Finding Max & Minimums4) Related Rates Problems5) PVA
We will do examples of these as warm ups over the next couple of days!
IntegralsIntegrals are Anti-Derivatives!
Applications of Integrals
1) Area between curve and x-axis2) Area between 2 curves3) Volumes of Solids4) Integrating a Rate to find a Total5) Average Value of a Function (Actually didn’t
cover… woops! We will though!)
We will do examples of these as warm ups over the next couple of days!
Integration methods
1) U-Substitution Reverse Chain Rule
2) Integration By Parts Reverse Product Rule
U-Sub Practice (Hint – Find the insides)
1)
2)
3)
Integration by Parts – 2 Functions being multiplied!
Given Find
Steps:1) Label f(x) and g’(x)2) Find their counterpart3) Plug in and Evaluate the Integral
Hardest Part: Labeling f(x)
Here is a HINT! This is NEW!!!!
Pick f(x) by L. I. A. T. E.
Examples
Coming Up! Calculus BC
Fancy FunctionsUnit 1: PolarUnit 2: Parametric & Vector
Unit 3: More Applications of Integrals
SeriesUnit 4: Infinite SeriesUnit 5: Power and Taylor Series