Calculus 1
University Study Guides
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 Limits4 min2.15.4. Limits2.15.5. Limits2.15.6. Limits2.15.7. Limits2.15.8. Limits2.15.9. Limits2.15.10. Limits: Indeterminate forms2.15.11. Limits3 min2.15.12. IVT2.15.13. IVT2.15.14. IVT5 min2.15.15. Fundamental Trig Limit5 min2.15.16. Fundamental Trig Limit3 min2.15.17. Squeeze Theorem1 min2.15.18. Squeeze Theorem4 min2.15.19. Squeeze Theorem2.15.20. Continuity
3. Derivatives
2.8hr3.20.1. Derivative by Definition3.20.2. Basic Derivatives3.20.3. Basic Derivatives1 min3.20.4. Derivative by Definition3.20.5. Chain Rule3.20.6. Chain Rule3.20.7. Quotient Rule10 min3.20.8. Quotient Rule2 min3.20.9. Power of a Function Rule2 min3.20.10. Implicit Differentiation3.20.11. Implicit Differentiation3.20.12. Second Derivative6 min3.20.13. Logarithmic Differentiation4 min3.20.14. Logarithmic Differentiation 3.20.15. Inverse Trigonometric Derivatives3.20.16. Tangent Lines3.20.17. Tangent Lines3.20.18. Horizontal Tangent Lines2 min3.20.19. Product Rule6 min3.20.20. Product Rule4 min3.20.21. Product Rule4 min3.20.22. Normal Line5 min
4. Applications of Differentiation
4hr4.20.1. Related Rates4.20.2. Related Rates5 min4.20.3. Related Rates5 min4.20.4. Linear Approximation4 min4.20.5. Linear Approximation4.20.6. Taylor Series from Definition7 min4.20.7. Taylor Polynomials4.20.8. Maclaurin Polynomial4.20.9. Newton's Method2 min4.20.10. 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 Theorem1 min4.20.21. Rolle's Theorem6 min4.20.22. MVT4.20.23. MVT2 min4.20.24. MVT3 min4.20.25. MVT4.20.26. Intervals of Increase and Decrease4.20.27. Intervals of Increase and Decrease3 min4.20.28. Critical Points6 min4.20.29. Critical Points1 min4.20.30. Extrema5 min4.20.31. Extrema6 min4.20.32. Second Derivative Test10 min4.20.33. Curve Sketching4.20.34. Curve Sketching12 min4.20.35. 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
2.7hr7.15.1. Antiderivatives: Indefinite Integrals7.15.2. Indefinite Integral with Trig and Inverse Trig7.15.3. Definite Integral with Trig1 min7.15.4. Integration by Substitution7.15.5. Integration by Substitution2 min7.15.6. Integration by Substitution3 min7.15.7. Integration by Substitution3 min7.15.8. Computing Integrals3 min7.15.9. Finite Sums3 min7.15.10. Finite Sums7.15.11. Finite Sums7.15.12. Riemann Sums7.15.13. Riemann Sums7.15.14. Riemann Sums7.15.15. Integral from Definition3 min7.15.16. Integral from Definition7.15.17. Definite Integral2 min7.15.18. Substitution with Definite Integral3 min7.15.19. Integration7.15.20. Definite Integral7.15.21. FTC I7.15.22. FTC I7.15.23. FTC I
8. Applications of Integration
1.8hr8.8.1. Displacement, Velocity, and Acceleration3 min8.8.2. Position, Velocity and Acceleration 2 min8.8.3. Position, Velocity and Acceleration 3 min8.8.4. Average Value of a Function2 min8.8.5. Average Value of a Function8.8.6. Average Function Value of a Function1 min8.8.7. Area Between Curves8.8.8. Area Between Curves4 min8.8.9. Area Between Curves8.8.10. Area Between Curves8.8.11. Volumes of Revolution, Cylindrical Shells8.8.12. Volumes of Revolution, Disc/Washer4 min8.8.13. Volumes of Revolution, Cylindrical Shells8.8.14. Volumes of Revolution9 min8.8.15. Arc Length4 min8.8.16. Arc Length4 min8.8.17. Arc Length with Partial Fractions7 min8.8.18. Arc Length with Perfect Square4 min8.8.19. Surface Area6 min8.8.20. Surface Area5 min
9. Applications of Integration for Physical Science
60min10. Integration Techniques
2.4hr10.10.1. Integration by Parts2 min10.10.2. Integration by Parts10.10.3. Integration by Parts10.10.4. Integration by Parts10.10.5. Integration by Parts10.10.6. Trigonometric Integral3 min10.10.7. Trigonometric Integral10.10.8. Trigonometric Integral with IBP5 min10.10.9. Trigonometric Substitution5 min10.10.10. Trigonometric Substitution6 min10.10.11. Trigonometric Substitution8 min10.10.12. Partial Fraction Decomposition8 min10.10.13. Partial Fraction Decomposition24 min10.10.14. Partial Fraction Decomposition4 min10.10.15. The Trapezoid Rule10.10.16. The Trapezoid Rule2 min10.10.17. Simpson's Rule
11. Additional Resources
12. 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.