MAC 2311
UCF
Course Overview
Lessons & Practice
I. Welcome
1. Pre-Calculus (Review)
3hr2. Limits and Derivatives
2.1hr2.17.1. One-sided Limits2.17.2. Limits2.17.3. Special Limits2.17.4. Limits2.17.5. Limits2.17.6. Limits2.17.7. Limits2.17.8. Limits2.17.9. Limits2.17.10. Limits: Indeterminate forms2.17.11. Limits2.17.12. IVT2.17.13. IVT2.17.14. IVT2.17.15. Fundamental Trig Limit2.17.16. Fundamental Trig Limit2.17.17. Squeeze Theorem2.17.18. Squeeze Theorem2.17.19. Squeeze Theorem2.17.20. Continuity
3. Differentiation Rules
3hr3.21.1. Derivative by Definition3.21.2. Basic Derivatives3.21.3. Basic Derivatives3.21.4. Derivative by Definition3.21.5. Chain Rule3.21.6. Chain Rule3.21.7. Quotient Rule3.21.8. Quotient Rule3.21.9. Power of a Function Rule3.21.10. Implicit Differentiation3.21.11. Implicit Differentiation3.21.12. Second Derivative3.21.13. Logarithmic Differentiation3.21.14. Logarithmic Differentiation 3.21.15. Inverse Trigonometric Derivatives3.21.16. Tangent Lines3.21.17. Tangent Lines3.21.18. Horizontal Tangent Lines3.21.19. Product Rule3.21.20. Product Rule3.21.21. Product Rule3.21.22. Normal Line
4. Applications of Differentiation
4hr4.20.1. Related Rates4.20.2. Related Rates4.20.3. Related Rates4.20.4. Linear Approximation4.20.5. Linear Approximation4.20.6. Taylor Series from Definition4.20.7. Taylor Polynomials4.20.8. Maclaurin Polynomial4.20.9. Newton's Method4.20.10. Newton's Method4.20.11. L'Hopital's Rule4.20.12. L'Hopital's Rule4.20.13. L'Hopital's Rule4.20.14. Limits4.20.15. L'Hopital's Rule4.20.16. L'Hopital's Rule4.20.17. Limits4.20.18. Limits4.20.19. Extreme Value Theorem4.20.20. Rolle's Theorem4.20.21. Rolle's Theorem4.20.22. MVT4.20.23. MVT4.20.24. MVT4.20.25. MVT4.20.26. Intervals of Increase and Decrease4.20.27. Intervals of Increase and Decrease4.20.28. Critical Points4.20.29. Critical Points4.20.30. Extrema4.20.31. Extrema4.20.32. Second Derivative Test4.20.33. Curve Sketching4.20.34. Curve Sketching4.20.35. Curve Sketching4.20.36. Optimization4.20.37. Optimization4.20.38. Optimization
5. Applications of Differentiation for Science
41min6. Applications of Differentiation for Business & Econ
42min7. Integrals
2.3hr7.11.1. Antiderivatives: Indefinite Integrals7.11.2. Indefinite Integral with Trig and Inverse Trig7.11.3. Definite Integral with Trig7.11.4. Integration by Substitution7.11.5. Integration by Substitution7.11.6. Integration by Substitution7.11.7. Integration by Substitution7.11.8. Computing Integrals7.11.9. Finite Sums7.11.10. Finite Sums7.11.11. Finite Sums7.11.12. Riemann Sums7.11.13. Riemann Sums7.11.14. Riemann Sums7.11.15. Integral from Definition7.11.16. Integral from Definition7.11.17. Definite Integral7.11.18. Substitution with Definite Integral7.11.19. Integration7.11.20. Definite Integral7.11.21. FTC I7.11.22. FTC I7.11.23. FTC I
8. Integration Techniques
2.4hr8.10.1. Integration by Parts8.10.2. Integration by Parts8.10.3. Integration by Parts8.10.4. Integration by Parts8.10.5. Integration by Parts8.10.6. Trigonometric Integral8.10.7. Trigonometric Integral8.10.8. Trigonometric Integral with IBP8.10.9. Trigonometric Substitution8.10.10. Trigonometric Substitution8.10.11. Trigonometric Substitution8.10.12. Partial Fraction Decomposition8.10.13. Partial Fraction Decomposition8.10.14. Partial Fraction Decomposition8.10.15. The Trapezoid Rule8.10.16. The Trapezoid Rule8.10.17. Simpson's Rule
9. 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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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.