MATH 1025

VT

Course Overview

Lessons & Practice

I. Welcome

1. Pre-Calculus (Review)

3hr

1.1.1. Interval Notation 4 min

1.1.2. Set Notation3 min

1.1.3. Example4 min

1.1.4. Practice2 min

1.1.5. Practice52 sec

1.1.6. Cheatsheet

1.2.1. Domain2 min

1.2.2. Range2 min

1.2.3. Example2 min

1.2.4. Practice 40 sec

1.2.5. Practice 3 min

1.3.1. Operations with Functions3 min

1.3.2. Example2 min

1.3.3. Practice2 min

1.3.4. Practice1 min

1.4.1. Even and Odd Functions3 min

1.4.2. Example2 min

1.5.1. Transformation of Graphs2 min

1.5.2. Example1 min

1.5.3. Practice2 min

1.6.1. Basic of Polynomials4 min

1.6.2. Example2 min

1.6.3. Practice3 min

1.6.4. Polynomial Graphs & Characteristics4 min

1.6.5. Example2 min

1.6.6. Practice2 min

1.7.1. Factoring 5 min

1.7.2. Factoring a Difference & Sum of Cubes3 min

1.7.3. Example2 min

1.7.4. Practice46 sec

1.7.5. Practice2 min

1.7.6. Practice2 min

1.8.1. Dividing Polynomials - Long Division6 min

1.8.2. Example3 min

1.8.3. Dividing Polynomials - Synthetic Division8 min

1.8.4. Example2 min

1.8.5. Practice2 min

1.8.6. Practice3 min

1.9.1. Rational Functions4 min

1.9.2. Solving Rational Equations3 min

1.9.3. Example5 min

1.9.4. Example3 min

1.9.5. Practice6 min

1.9.6. Practice2 min

1.10.1. Radical Functions59 sec

1.10.2. Solving Radical Equations5 min

1.10.3. Example5 min

1.10.4. Practice8 min

1.11.1. Piecewise Functions4 min

1.11.2. Example5 min

1.11.3. Practice3 min

1.12.1. Absolute Value Function1 min

1.12.2. Example3 min

1.13.1. Inverse Functions3 min

1.13.2. Example3 min

1.13.3. Practice2 min

1.14.1. Exponential Functions3 min

1.14.2. Example1 min

1.14.3. Example2 min

1.15.1. Logarithmic Functions4 min

1.15.2. Example3 min

1.15.3. Example:3 min

1.15.4. Practice2 min

1.16.1. Trigonometric Functions6 min

1.16.2. Example4 min

1.16.3. Trig Identities2 min

1.16.4. Practice3 min

1.16.5. Practice4 min

1.17.1. Inverse Trigonometric Functions4 min

1.17.2. Example3 min

1.17.3. Practice2 min

1.17.4. Practice2 min

2. Approximate Rate of Change at a Point

59min

2.1.1. Average Rate of Change & the Secant Line2 min

2.1.3. Practice Level 12 min

2.1.4. Practice Level 2

2.1.5. Practice Level 3

2.2.1. Instantaneous Rate of Change & the Tangent Line4 min

2.2.2. Example2 min

2.2.3. Practice Level 1

2.2.4. Practice Level 2

2.2.5. Practice Level 3

2.3.1. Derivatives as a Rate of Change2 min

2.3.2. Average Rate of Change46 sec

2.3.3. Example2 min

2.3.4. Practice1 min

2.4.1. Limit Basics2 min

2.4.2. Example1 min

2.5.1. Limit Laws 2 min

2.5.2. Practice1 min

2.6.1. One-Sided Limits2 min

2.6.2. Example: One-Sided Limit2 min

2.6.3. Practice: One-Sided Limits3 min

2.7.1. Limits at Infinity3 min

2.7.2. Example60 sec

2.7.3. Example3 min

2.7.4. Example4 min

2.7.5. Practice 3 min

2.7.6. Practice3 min

2.8.1. Computing Limits by Factoring1 min

2.8.2. Example1 min

2.8.3. Practice2 min

2.9.1. The Limit Definition of a Derivative2 min

2.9.2. Example3 min

2.9.3. Practice5 min

2.9.4. When is Function Not Differentiable?

3. Derivative as a Function

2.3hr

3.1.1. Differentiation Laws51 sec

3.2.1. The Power Rule1 min

3.2.2. Example2 min

3.2.3. Practice51 sec

3.3.1. Tangent Lines1 min

3.3.2. Example3 min

3.3.3. Practice2 min

3.4.1. Normal Lines1 min

3.4.2. Example3 min

3.4.3. Practice1 min

3.5.1. The Product Rule49 sec

3.5.2. Example2 min

3.5.3. Example2 min

3.5.4. Practice2 min

3.6.1. The Quotient Rule1 min

3.6.2. Example2 min

3.6.3. Practice4 min

3.7.1. The Chain Rule1 min

3.7.2. Example2 min

3.7.3. Practice3 min

3.8.1. Derivatives of Trigonometric Functions1 min

3.8.2. Example39 sec

3.8.3. Example3 min

3.8.4. Example1 min

3.8.5. Practice3 min

3.8.6. Practice2 min

3.9.1. Derivatives of Exponential Functions1 min

3.9.2. Example52 sec

3.9.3. Example3 min

3.9.4. Practice1 min

3.10.1. Higher Order Derivatives2 min

3.10.2. Example3 min

3.10.3. Practice2 min

3.10.4. Practice2 min

3.11.1. Implicit Differentiation2 min

3.11.2. Example3 min

3.11.3. Example3 min

3.11.4. Practice3 min

3.12.1. Derivatives of Inverse Functions52 sec

3.12.2. Example2 min

3.12.3. Practice3 min

3.13.1. Derivatives of Logarithmic Functions1 min

3.13.2. Example56 sec

3.13.3. Example2 min

3.13.4. Practice2 min

3.13.5. Practice: Log and Ln2 min

3.14.1. Inverse Trig Derivatives1 min

3.14.2. Example1 min

3.14.3. Practice3 min

4. Analyzing Graphs

2.8hr

4.1.1. Intervals of Increase and Decrease1 min

4.1.2. Example2 min

4.1.3. Practice3 min

4.2.1. Critical Points and Extrema2 min

4.2.3. Practice3 min

4.3.1. 1st and 2nd Derivative Tests3 min

4.3.2. Example7 min

4.3.4. Practice3 min

4.4.1. Maximum and Minimum on Closed Intervals2 min

4.4.2. Example4 min

4.4.3. Practice3 min

4.4.4. Practice3 min

4.5.1. Concavity and Inflection Points56 sec

4.5.2. Example6 min

4.5.3. Practice6 min

4.6.1. Curve Sketching2 min

4.6.2. Example7 min

4.6.3. Practice9 min

4.6.4. Practice

4.7.1. Optimization1 min

4.7.2. Example4 min

4.7.3. Example4 min

4.7.4. Practice6 min

4.7.5. Practice4 min

4.8.1. Related Rates

4.8.2. Related Rates5 min

4.8.3. Related Rates5 min

4.8.4. Linear Approximation4 min

4.8.5. Linear Approximation

4.8.6. Taylor Series from Definition7 min

4.8.7. Taylor Polynomials

4.8.8. Maclaurin Polynomial

4.8.9. Newton's Method2 min

4.8.10. Newton's Method

4.8.11. L'Hopital's Rule

4.8.12. L'Hopital's Rule

4.8.13. L'Hopital's Rule

4.8.15. L'Hopital's Rule

4.8.16. L'Hopital's Rule

4.8.19. Extreme Value Theorem

4.8.20. Rolle's Theorem1 min

4.8.21. Rolle's Theorem6 min

4.8.23. MVT2 min

4.8.24. MVT3 min

4.8.26. Intervals of Increase and Decrease

4.8.27. Intervals of Increase and Decrease3 min

4.8.28. Critical Points6 min

4.8.29. Critical Points1 min

4.8.30. Extrema5 min

4.8.31. Extrema6 min

4.8.32. Second Derivative Test10 min

4.8.33. Curve Sketching

4.8.34. Curve Sketching12 min

4.8.35. Curve Sketching

4.8.36. Optimization

4.8.37. Optimization

4.8.38. Optimization

5. Differential Equations

1.2hr

5.1.1. Differential Equations8 min

5.1.2. Direction Fields/Slope Fields5 min

5.1.3. Practice Question: DE Solution Graphs3 min

5.2.1. Separable First Order Differential Equations3 min

5.2.2. Practice (separable DE)2 min

5.2.3. Practice (IVP)3 min

5.2.4. Practice (IVP)3 min

5.2.5. Practice (IVP*)5 min

5.2.6. Practice (separable DE)1 min

5.3.1. Linear First Order Differential Equations7 min

5.3.2. Practice (integrating factor)1 min

5.3.3. Practice (linear DE)3 min

5.3.4. Practice (IVP)3 min

5.3.5. Practice (IVP)4 min

5.4.1. Exponential Growth and Decay3 min

5.4.2. Example4 min

5.4.3. Example5 min

5.4.4. Practice5 min

5.4.5. Practice (population)3 min

5.4.6. Practice (population)4 min

5.5.1. Second-Order Reducible DE

5.5.2. Practice: Dependent Variable Missing

5.5.3. Practice: Independent Variable Missing

5.Q. DE Quiz4 Qns

I Welcome

Free Activity

Welcome to Integral Calculus!
My name is Corey and I'm the instructor for this course. Feel free to go through this course at your own pace.
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Answered

L

Layan E

Use the Intermediate Value Theorem to show that thereis a root of the given equation in the specified interval.Use the Intermediate Value Theorem to show that thereis a root of the given equation in the specified interval.
sin(x)=x2−x, x∈(1,2)

C

Corey M

Instructor

While this isn't quite the place for this question (please refer to the IVT section in the course), and we can't really just solve random problems for you, I can give you a bit of a hint:  You could try moving everything to one side of the equation and treating it like a function, and then see if you can't find function values within your specified range that return a positive value and a negative value (another hint: try the endpoints of your interval first).  If you're able to do that, then the IVT tells us that there should exist a function input between those two points that returns 0 or, in other words, that is a root.

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