MATH-1524
VT
Course Overview
Lessons & Practice
I. Welcome
1. Functions
3hr2. Business Terminology
2hr2.1.1. Cost, Price, Revenue, and Profit1 min2.1.2. Supply and Demand2 min2.1.3. Marginal & Average Cost, Revenue and Profit1 min2.1.4. Example: Average Rate of Change of Cost2 min2.1.5. Practice: Average Profit4 min2.1.6. Example: Marginal Cost2 min2.1.7. Practice: Marginal Revenue given Price Function2 min2.1.8. Practice: Marginal Revenue and Profit7 min
3. Applications of Exponential Functions
2.2hr4. Rates of Change
1.7hr4.9.1. Derivative by Definition4.9.2. Basic Derivatives4.9.3. Basic Derivatives1 min4.9.4. Derivative by Definition4.9.5. Chain Rule4.9.6. Chain Rule4.9.7. Quotient Rule10 min4.9.8. Quotient Rule2 min4.9.9. Power of a Function Rule2 min4.9.10. Implicit Differentiation4.9.11. Implicit Differentiation4.9.12. Second Derivative6 min4.9.13. Logarithmic Differentiation4 min4.9.14. Logarithmic Differentiation 4.9.15. Inverse Trigonometric Derivatives4.9.16. Tangent Lines4.9.17. Tangent Lines4.9.18. Horizontal Tangent Lines2 min4.9.19. Product Rule6 min4.9.20. Product Rule4 min4.9.21. Product Rule4 min4.9.22. Normal Line5 min
5. Derivative Rules
1.8hr5.11.1. Derivative by Definition5.11.2. Basic Derivatives5.11.3. Basic Derivatives1 min5.11.4. Derivative by Definition5.11.5. Chain Rule5.11.6. Chain Rule5.11.7. Quotient Rule10 min5.11.8. Quotient Rule2 min5.11.9. Power of a Function Rule2 min5.11.10. Implicit Differentiation5.11.11. Implicit Differentiation5.11.12. Second Derivative6 min5.11.13. Logarithmic Differentiation4 min5.11.14. Logarithmic Differentiation 5.11.15. Inverse Trigonometric Derivatives5.11.16. Tangent Lines5.11.17. Tangent Lines5.11.18. Horizontal Tangent Lines2 min5.11.19. Product Rule6 min5.11.20. Product Rule4 min5.11.21. Product Rule4 min5.11.22. Normal Line5 min
6. Graphing Applications of Derivatives
5hr6.17.1. Related Rates6.17.2. Related Rates5 min6.17.3. Related Rates5 min6.17.4. Linear Approximation4 min6.17.5. Linear Approximation6.17.6. Taylor Series from Definition7 min6.17.7. Taylor Polynomials6.17.8. Maclaurin Polynomial6.17.9. Newton's Method2 min6.17.10. Newton's Method6.17.11. L'Hopital's Rule6.17.12. L'Hopital's Rule6.17.13. L'Hopital's Rule6.17.14. Limits6.17.15. L'Hopital's Rule6.17.16. L'Hopital's Rule6.17.17. Limits6.17.18. Limits6.17.19. Extreme Value Theorem6.17.20. Rolle's Theorem1 min6.17.21. Rolle's Theorem6 min6.17.22. MVT6.17.23. MVT2 min6.17.24. MVT3 min6.17.25. MVT6.17.26. Intervals of Increase and Decrease6.17.27. Intervals of Increase and Decrease3 min6.17.28. Critical Points6 min6.17.29. Critical Points1 min6.17.30. Extrema5 min6.17.31. Extrema6 min6.17.32. Second Derivative Test10 min6.17.33. Curve Sketching6.17.34. Curve Sketching12 min6.17.35. Curve Sketching6.17.36. Optimization6.17.37. Optimization6.17.38. Optimization
7. Functions of Several Variables
1.8hr8. 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.
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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
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.