APSC 171
Queen's
Course Overview
Grade Boosters
Lessons & Practice
I. Welcome
1. Derivatives
3hr1.1.1. Basic Differentiation Rules7 min1.1.2. Example: Derivative of a polynomial6 min1.1.3. Derivatives of Exponential and Trigonometric Functions5 min1.1.4. Example: Differentiating more complex functions7 min1.1.5. Practice: Differentiating functions 13 min1.1.6. Practice: Differentiating functions 22 min
2. Vector-Valued Functions
2.9hr2.3.1. Parametric Curves in 3D2 min2.3.2. Graphing Planar Curves and Space Curves6 min2.3.3. Eliminating Parameters3 min2.3.4. Example: Sketching two-dimensional vector-valued functions7 min2.3.5. Example: Eliminating a parameter6 min2.3.6. Example: Parallel vectors8 min2.3.7. Practice: Graphing a Vector-Valued Function15 min2.3.8. Practice: Determining Vector-Valued Functions with conditions12 min
2.4.1. Inverse Functions7 min2.4.2. Inverse Trigonometric Functions13 min2.4.3. Example: Computing inverse trigonometric functions of numbers4 min2.4.4. Example: Computing inverses of the same trigonometric function10 min2.4.5. Example: Computing trigonometric functions of different inverse trigonometric functions.5 min2.4.6. Practice: Inverse Trigonometric Functions 12 min2.4.7. Practice: Inverse Trigonometric Functions 210 min
3. Derivatives of Vector Valued Functions
2hr3.2.1. Equations of Lines in 6 min3.2.2. Example: Equations of Lines in 8 min3.2.3. Practice: Equations of Lines in 3.2.4. Equations of Planes in 7 min3.2.5. Example: Equations of Planes in 5 min3.2.6. Practice: Equations of Planes in 3.2.7. Distance Between a Point and a Plane4 min3.2.8. Example: Distance Between a Point and a Plane7 min3.2.9. Practice: Distance Between a Point and a Plane3.2.10. Distance Between a Point and a Line5 min3.2.11. Example: Distance Between a Point and a Line8 min3.2.12. Practice: Distance Between a Point and a Line3.2.13. Closest Point on a Plane8 min
3.3.1. Norm of a Vector7 min3.3.2. Example: Norm of a Vector6 min3.3.3. Practice: Norm of a Vector3.3.4. Dot Product5 min3.3.5. Example: Dot product5 min3.3.6. Properties of the Dot Product5 min3.3.7. Example: Properties of the Dot Product8 min3.3.8. Practice: Properties of the Dot Product3.3.9. Projections6 min3.3.10. Example: Projections6 min3.3.11. Practice: Projections3.3.12. Practice: Projections3.3.13. Practice: Projections
4. Applications of Differentiation
1.2hr5. Integrals
1hr6. Integration Techniques
47min7. Applications of Integration
48min8. Differential Equations
1.5hr9. Complex Numbers
1.4hrI Welcome
Free Activity
Test 1 Mock
I
Ingrid W
0 secs
Releases: May 25, 12:09am
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.