MA 16010
Purdue
Course Overview
Lessons & Practice
I. Welcome
1. Pre-Calculus (Review)
3hr2. Limits
1.9hr2.15.1. One-sided Limits2.15.2. Limits2.15.3. Special Limits2.15.4. Limits2.15.5. Limits2.15.6. Limits2.15.7. Limits2.15.8. Limits2.15.9. Limits2.15.10. Limits: Indeterminate forms2.15.11. Limits2.15.12. IVT2.15.13. IVT2.15.14. IVT2.15.15. Fundamental Trig Limit2.15.16. Fundamental Trig Limit2.15.17. Squeeze Theorem2.15.18. Squeeze Theorem2.15.19. Squeeze Theorem2.15.20. Continuity
3. Derivatives
2.8hr3.20.1. Derivative by Definition3.20.2. Basic Derivatives3.20.3. Basic Derivatives3.20.4. Derivative by Definition3.20.5. Chain Rule3.20.6. Chain Rule3.20.7. Quotient Rule3.20.8. Quotient Rule3.20.9. Power of a Function Rule3.20.10. Implicit Differentiation3.20.11. Implicit Differentiation3.20.12. Second Derivative3.20.13. Logarithmic Differentiation3.20.14. Logarithmic Differentiation 3.20.15. Inverse Trigonometric Derivatives3.20.16. Tangent Lines3.20.17. Tangent Lines3.20.18. Horizontal Tangent Lines3.20.19. Product Rule3.20.20. Product Rule3.20.21. Product Rule3.20.22. 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. Differential Equations
1.2hr8. Integrals
2.7hr8.15.1. Antiderivatives: Indefinite Integrals8.15.2. Indefinite Integral with Trig and Inverse Trig8.15.3. Definite Integral with Trig8.15.4. Integration by Substitution8.15.5. Integration by Substitution8.15.6. Integration by Substitution8.15.7. Integration by Substitution8.15.8. Computing Integrals8.15.9. Finite Sums8.15.10. Finite Sums8.15.11. Finite Sums8.15.12. Riemann Sums8.15.13. Riemann Sums8.15.14. Riemann Sums8.15.15. Integral from Definition8.15.16. Integral from Definition8.15.17. Definite Integral8.15.18. Substitution with Definite Integral8.15.19. Integration8.15.20. Definite Integral8.15.21. FTC I8.15.22. FTC I8.15.23. FTC I
9. Applications of Integration
1.8hr9.8.1. Displacement, Velocity, and Acceleration9.8.2. Position, Velocity and Acceleration 9.8.3. Position, Velocity and Acceleration 9.8.4. Average Value of a Function9.8.5. Average Value of a Function9.8.6. Average Function Value of a Function9.8.7. Area Between Curves9.8.8. Area Between Curves9.8.9. Area Between Curves9.8.10. Area Between Curves9.8.11. Volumes of Revolution, Cylindrical Shells9.8.12. Volumes of Revolution, Disc/Washer9.8.13. Volumes of Revolution, Cylindrical Shells9.8.14. Volumes of Revolution9.8.15. Arc Length9.8.16. Arc Length9.8.17. Arc Length with Partial Fractions9.8.18. Arc Length with Perfect Square9.8.19. Surface Area9.8.20. Surface Area
10. Applications of Integration for Physical Science
60min11. Integration Techniques
2.4hr11.10.1. Integration by Parts11.10.2. Integration by Parts11.10.3. Integration by Parts11.10.4. Integration by Parts11.10.5. Integration by Parts11.10.6. Trigonometric Integral11.10.7. Trigonometric Integral11.10.8. Trigonometric Integral with IBP11.10.9. Trigonometric Substitution11.10.10. Trigonometric Substitution11.10.11. Trigonometric Substitution11.10.12. Partial Fraction Decomposition11.10.13. Partial Fraction Decomposition11.10.14. Partial Fraction Decomposition11.10.15. The Trapezoid Rule11.10.16. The Trapezoid Rule11.10.17. Simpson's Rule
I Welcome
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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.