## Math 229

Our five-minute videos illustrate how to solve a variety of equations used in Math 229. Browse our lecture notes to get detailed explanations, and take past exams to prepare for this year's exam. If you're seeking in-person tutoring, stop by the Mathematics Assistance Center in DuSable Hall, room 326. Our tutoring schedule has a range of Math 229 tutoring times to fit your schedule.

### Practice Exams and Final

### Videos and Tutorials

- Evaluating limits numerically.
- Evaluating limits from a graph.
- What are one-sided limits?
- Sketch a graph satisfying limit conditions.
- Find the slope of the tangent line using limits.
- Evaluate limits by direct substitution.
- Evaluate limits multiplying by a conjugate.
- Evaluate limits by factoring.
- Evaluate limits by simplifying.
- Evaluate limits by finding a common denominator - example 1.
- Evaluate limits by using a common denominator - example 2.
- Introduction to continuity - the three conditions.
- Where is f(x) continuous? Example 1.
- Where is f(x) continuous? Example 2.

##### Evaluating Limits Numerically

##### Evaluating Limits from a Graph

##### What are one-sided limits?

**Example**

When \(a \neq 0\), there are two solutions to \(ax^2+bx+c=0\) and they are $$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$$

##### Sketch a Graph Satisifying Limit Conditions

##### Find the Slope of the Tangent Line Using Limits

##### Evaluate Limits - by Direct Substitution

##### Evaluate Limits - Multiplying by a Conjugate

##### Evaluate Limits - by Factoring

##### Evaluate Limits - by Simplifying

##### Evaluate Limits by Finding a Common Denominator - Example 1

##### Evaluate Limits by using a Common Denominator - Example 2

##### Introduction to Continuity - the 3 Conditions

##### Where is f(x) continuous? Example 1

##### Where is f(x) continuous? Example 2

- Find slope of the tangent line using limit definition.
- Find slope of the tangent line using limit definition - example 2.
- Find slope of the tangent line using limit definition - example 3.
- Sketch the graph of the derivative.
- Different notations for derivatives.
- Derivatives using the power rule.
- Derivatives using the product rule - example 1.
- Derivatives using the product rule - example 2.
- Derivative using product rule for three functions.
- Derivatives using the quotient rule - example 1.
- Graphical proof of the derivative of sin(x).
- Derivative of the trig functions.
- Extended power rule for derivatives.
- Derivative using the chain and product rule - example 1.
- Derivative using chain rule - example 2.
- Chain rule - composition of three functions - example 3.
- Derivative using the chain rule - example 4.
- First and second derivatives using the chain rule - example 5.
- Equation of the tangent line using the chain rule - example 6.
- Related rates - area of circle - example 1.
- Related rates - sphere - example 2.
- Related rates - shadow - example 3.
- Related rates - example 4A (rocket) .
- Related rates - example 4B (rocket).
- Implicit differentiation - introduction - example 1.
- Implicit differentiation - example 2.
- Implicit differentiation - example 3.
- Implicit differentiation - example 4.

##### Find Slope of the Tangent Line Using Limit Definition

##### Find Slope of the Tangent Line Using Limit Definition - Example 2

##### Find Slope of the Tangent Line Using Limit Definition - Example 3

##### Sketch the Graph of the Derivative

##### Different Notations for Derivatives

##### Derivatives Using the Power Rule

##### Derivatives Using the Product Rule - Example 1

##### Derivatives Using the Product Rule - Example 2

##### Derivative Using Product Rule for 3 Functions

##### Derivatives Using the Quotient Rule - Example 1

##### Graphical Proof of the Derivative of sin(x)

##### Derivative of the Trig Functions

##### Extended Power Rule for Derivatives

##### Derivative Using the Chain and Product Rule - Example 1

##### Derivative Using Chain Rule - Example 2

##### Chain Rule - Composition of Three Functions - Example 3

##### Derivative Using the Chain Rule - Example 4

##### First and Second Derivatives Using the Chain Rule - Example 5

##### Equation of the Tangent Line Using the Chain Rule - Example 6

##### Related Rates - Area of Circle - Example 1

##### Related Rates - Sphere - Example 2

##### Related Rates - Shadow - Example 3

##### Related Rates - Example 4A (Rocket)

##### Related Rates - Example 4B (Rocket)

##### Implicit Differentiation - Introduction - Example 1

##### Implicit Differentiation - Example 2

##### Implicit Differentiation - Example 3

##### Implicit Differentiation - Example 4

### Lecture Notes

- 3.1 Find max and minimum values, extreme value theorem, Fermat's theorem.
- 3.2 The mean value theorem.
- 3.3 Using derivatives to analyze a function, first derivative test.
- 3.4 Limits at infinity, asymptotes, sketching curves.
- 3.5 Summary of curve sketching with step-by-step instructions.
- Curve sketching steps.
- 3.7 Optimization.
- 3.8 Newton's method.
- 3.9 Antiderivatives.

### Handouts and Study Material

### Contact

**Brian Veitch**

Instructor

Director of Mathematics Assistance Center

815-753-6755

bveitch@niu.edu