# Calculus I

Syllabus

Schedule

Review Test 1

Review Test 2 (please disregard exercises 40 thru 43 from this review)

Review Test 3

Lecture Notes

Notes

Model

Exercises

Related Rates and Tangent to a CurveME 1
Limits of a Function and Limit LawsME 2
One-Side LimitME 3
ContinuityME 4
Limits Involving Infinity; Asymptotes of GraphsME 5
Tangents and the Derivatives at a PointME 6
The Derivative as a FunctionME 7
Differentiation RulesME 8
The Derivative as a Rate of ChangeME 9
Derivatives of Trigonometric FunctionsME 10
The Chain RuleME 11
Implicit DifferentiationME 12
Related RatesME 13
Extreme Values of FunctionsME 14
The Mean Values TheoremME 15
Monotonic Functions and The First Derivative TestME 16
Concavity and Curve SketchingME 17
Applied OptimizationME 18
AntiderivativesME 19
Area and Estimating with Finite SumsME 20
The Definite IntegralME 21
The Fundamental Theorem of CalculusME 22
Indefinite Integrals and the Substitution MethodME 23
Area Between CurvesME 24

Objectives

Objectives

Model

Exercises

Practice

Exercises

Find the limit of a function using limit theorems.ME 1PE 1
Compute left and right hand limitsME 2PE 2
Calculate limits involving infinityME 3PE 3
Find intervals upon which a function is continuousME 4PE 4
Compute limits involving trigonometric functionsME 5PE 5
Find the slope of a tangent line using the limit definition of the derivative.ME 6PE 6
Determine where a given function is not continuous, not differentiable, or bothME 7PE 7
Use the product and quotient rules to find a derivativeME 8PE 8
Apply the chain rule to find a derivativeME 9PE 9
Find the derivative of a function implicitlyME 10PE 10
Use implicit differentiation to solve related rates problems.ME 11PE 11
Use the derivative to locate and classify local extremaME 12PE 12
Use the second derivative to determine concavityME 13PE 13
Find the antiderivative of a functionME 14PE 14
Use the Fundamental Theorem of Calculus to compute a definite integralME 15PE 15
Use the substitution method of compute a definite integralME 16PE 16
Compute the area between two curvesME 17PE 17

Graphing Calculator Tutorials

The Graph of the function
Limit
One -side Limits
Limits at Infinity
Infinite Limits
Derivative
Tangent Lines
Graph of a Function
Definite Integral
Area
Area Between Curves

POWER POINTS

2. Limits.pptx
4. Limits of Trigonometric Functions.pptx
5. One – Side Limits.pptx
6. Continuity.pptx
7. Infinite Limits.pptx
8. The Derivative.pptx
9. Differentiability and Continuity.pptx
10. The Basic Differentiation Rules.pptx
11. The Product and Quotient Rules.pptx
12. The Chain Rule
13. The Instantaneous Rate of Change
14. Implicit Differentiation
15. Related Rates
16. Extrema on an Interval
17. The Mean Value Theorem
18. Increasing Decreasing Intervals and First Derivative Test
19. Concavity and the Second Derivative Test
20. The Graph of a Function
21 Optimization
22. Antiderivatives
23. Area and Definite Integrals
24. The Fundamental Theorem of Calculus
25. Integration by Substitution
26. Area Between Curves