MATH 102
UVIC
Course Overview
Lessons & Practice
I. Welcome
1. Non-Linear Functions
2.4hr1.2.1. Review of Quadratic Equations4 min1.2.2. General Transformations8 min1.2.3. Example3 min1.2.4. Practice (Level 1)1 min1.2.5. Translations4 min1.2.6. Example4 min1.2.7. Practice (Level 1)1 min1.2.8. Practice (Level 2)2 min1.2.9. Practice (Level 3)2 min1.2.10. Reflections3 min1.2.11. Example4 min1.2.12. Practice (Level 1)56 sec1.2.13. Practice (Level 2)2 min1.2.14. Practice (Level 3)1 min1.2.15. Applying Transformations7 min1.2.16. Example6 min1.2.17. Practice (Level 1)2 min
1.3.1. Basic of Polynomials4 min1.3.2. Example2 min1.3.3. Practice3 min1.3.4. Polynomial Graphs & Characteristics4 min1.3.5. Example2 min1.3.6. Practice2 min1.3.7. Factoring 5 min1.3.8. Factoring a Difference & Sum of Cubes3 min1.3.9. Example2 min1.3.10. Practice46 sec1.3.11. Practice2 min1.3.12. Practice2 min1.3.13. Rational Functions4 min1.3.14. Solving Rational Equations3 min1.3.15. Example5 min1.3.16. Example3 min1.3.17. Practice6 min1.3.18. Practice2 min
2. The Derivative
2.1hr2.1.1. Limit Basics2 min2.1.2. Example1 min2.1.3. Limit Laws 2 min2.1.4. Practice1 min2.1.5. One-Sided Limits2 min2.1.6. Example: One-Sided Limit2 min2.1.7. Practice: One-Sided Limits3 min2.1.8. Infinite Limits2 min2.1.9. Example1 min2.1.10. Example3 min2.1.11. Limits at Infinity3 min2.1.12. Example60 sec2.1.13. Example3 min2.1.14. Example4 min2.1.15. Practice 3 min2.1.16. Practice3 min2.1.17. Computing Limits by Factoring1 min2.1.18. Example1 min2.1.19. Practice2 min2.1.20. Computing Limits by Multiplying by the Conjugate3 min2.1.21. Example3 min2.1.22. Practice3 min2.1.23. Computing Limits by Getting a Common Denominator1 min2.1.24. Example2 min2.1.25. Practice4 min2.1.26. The Squeeze Theorem2 min2.1.27. Example2 min2.1.28. Practice2 min2.1.29. The Intermediate Value Theorem2 min2.1.30. Example2 min2.1.31. Practice2 min
2.6.1. One-sided Limits2.6.2. Limits2.6.3. Special Limits4 min2.6.4. Limits2.6.5. Limits2.6.6. Limits2.6.7. Limits2.6.8. Limits2.6.9. Limits2.6.10. Limits: Indeterminate forms2.6.11. Limits3 min2.6.12. IVT2.6.13. IVT2.6.14. IVT5 min2.6.15. Fundamental Trig Limit5 min2.6.16. Fundamental Trig Limit3 min2.6.17. Squeeze Theorem1 min2.6.18. Squeeze Theorem4 min2.6.19. Squeeze Theorem2.6.20. Continuity
3. Calculating the Derivative
1.5hr3.7.1. Derivative by Definition3.7.2. Basic Derivatives3.7.3. Basic Derivatives1 min3.7.4. Derivative by Definition3.7.5. Chain Rule3.7.6. Chain Rule3.7.7. Quotient Rule10 min3.7.8. Quotient Rule2 min3.7.9. Power of a Function Rule2 min3.7.10. Implicit Differentiation3.7.11. Implicit Differentiation3.7.12. Second Derivative6 min3.7.13. Logarithmic Differentiation4 min3.7.14. Logarithmic Differentiation 3.7.15. Inverse Trigonometric Derivatives3.7.16. Tangent Lines3.7.17. Tangent Lines3.7.18. Horizontal Tangent Lines2 min3.7.19. Product Rule6 min3.7.20. Product Rule4 min3.7.21. Product Rule4 min3.7.22. Normal Line5 min
4. Graphs and The Derivative
1.1hr5. Applications of The Derivative
3hr5.7.1. Related Rates5.7.2. Related Rates5 min5.7.3. Related Rates5 min5.7.4. Linear Approximation4 min5.7.5. Linear Approximation5.7.6. Taylor Series from Definition7 min5.7.7. Taylor Polynomials5.7.8. Maclaurin Polynomial5.7.9. Newton's Method2 min5.7.10. Newton's Method5.7.11. L'Hopital's Rule5.7.12. L'Hopital's Rule5.7.13. L'Hopital's Rule5.7.14. Limits5.7.15. L'Hopital's Rule5.7.16. L'Hopital's Rule5.7.17. Limits5.7.18. Limits5.7.19. Extreme Value Theorem5.7.20. Rolle's Theorem1 min5.7.21. Rolle's Theorem6 min5.7.22. MVT5.7.23. MVT2 min5.7.24. MVT3 min5.7.25. MVT5.7.26. Intervals of Increase and Decrease5.7.27. Intervals of Increase and Decrease3 min5.7.28. Critical Points6 min5.7.29. Critical Points1 min5.7.30. Extrema5 min5.7.31. Extrema6 min5.7.32. Second Derivative Test10 min5.7.33. Curve Sketching5.7.34. Curve Sketching12 min5.7.35. Curve Sketching5.7.36. Optimization5.7.37. Optimization5.7.38. Optimization
6. Integration
2.6hr6.1.1. Antiderivatives (Indefinite Integral)3 min6.1.2. Example2 min6.1.3. Practice1 min6.1.4. Practice1 min6.1.5. Practice1 min6.1.6. Antiderivatives (Indefinite Integral) of Exponential Functions1 min6.1.7. Example42 sec6.1.8. Practice1 min6.1.9. Practice2 min6.1.10. Antiderivatives (Indefinite Integral) of 2 min6.1.11. Example2 min6.1.12. Practice1 min
6.3.1. Approximating Areas & Riemann Sums 3 min6.3.2. Example4 min6.3.3. Practice3 min6.3.4. The Definite Integrals & Area Under a Curve2 min6.3.5. Example7 min6.3.6. Practice2 min6.3.7. Practice12 min6.3.8. Properties of the Definite Integral2 min6.3.9. Practice2 min6.3.10. Practice2 min6.3.11. Computing Definite Integrals Geometrically44 sec6.3.12. Example1 min6.3.13. Practice1 min
6.8.1. Antiderivatives: Indefinite Integrals6.8.2. Indefinite Integral with Trig and Inverse Trig6.8.3. Definite Integral with Trig1 min6.8.4. Integration by Substitution6.8.5. Integration by Substitution2 min6.8.6. Integration by Substitution3 min6.8.7. Integration by Substitution3 min6.8.8. Computing Integrals3 min6.8.9. Finite Sums3 min6.8.10. Finite Sums6.8.11. Finite Sums6.8.12. Riemann Sums6.8.13. Riemann Sums6.8.14. Riemann Sums6.8.15. Integral from Definition3 min6.8.16. Integral from Definition6.8.17. Definite Integral2 min6.8.18. Substitution with Definite Integral3 min6.8.19. Integration6.8.20. Definite Integral6.8.21. FTC I6.8.22. FTC I6.8.23. FTC I
7. Differential Equations
1.2hrI 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.
- Use the table of contents 📃 on the left to skip to parts you need help with
- Watch the video ▶ or read the written lessons 📖
- Speed up ⏩ or slow down ⏪ the videos
- Use the "Ask a question"❓ feature below each lesson/question any time!
Happy Studying!
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
InstructorWhile 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.