An example 3. Limits 4. The Derivative Function 5. Properties of Functions 3 Rules for Finding Derivatives 1. The Power Rule 2. Linearity of the Derivative 3. The Product Rule 4. The Quotient Rule 5. The Chain Rule 4 Transcendental Functions 1. Trigonometric Functions 2. A hard limit 4. Derivatives of the Trigonometric Functions 6. Exponential and Logarithmic functions 7. Derivatives of the exponential and logarithmic functions 8.
Implicit Differentiation 9. Inverse Trigonometric Functions Limits revisited Hyperbolic Functions 5 Curve Sketching 1. Maxima and Minima 2. The first derivative test 3. The second derivative test 4. Concavity and inflection points 5. Optimization 2. Related Rates 3. Newton's Method 4. Linear Approximations 5. The Mean Value Theorem 7 Integration 1. Two examples 2. The Fundamental Theorem of Calculus 3. Some Properties of Integrals 8 Techniques of Integration 1.
Substitution 2. Powers of sine and cosine 3. Trigonometric Substitutions 4. Integration by Parts 5. Rational Functions 6. Numerical Integration 7. Additional exercises 9 Applications of Integration 1.
Area between curves 2. Distance, Velocity, Acceleration 3. Volume 4. Average value of a function 5. Work 6. Center of Mass 7. Kinetic energy; improper integrals 8. Probability 9. Arc Length Polar Coordinates 2. Slopes in polar coordinates 3. Areas in polar coordinates 4. Parametric Equations 5. Calculus with Parametric Equations 11 Sequences and Series 1.
Sequences 2. Series 3. The Integral Test 4. Alternating Series 5. Comparison Tests 6. Absolute Convergence 7. The Ratio and Root Tests 8. Power Series 9. Calculus with Power Series Taylor Series Taylor's Theorem Additional exercises 12 Three Dimensions 1.
The Coordinate System 2. Vectors 3. The Dot Product 4. The Cross Product 5. Lines and Planes 6. Other Coordinate Systems 13 Vector Functions 1. Space Curves 2. Calculus with vector functions 3. Arc length and curvature 4. Motion along a curve 14 Partial Differentiation 1. Functions of Several Variables 2. Limits and Continuity 3. Partial Differentiation 4. The Chain Rule 5. Directional Derivatives 6. Add a comment. Active Oldest Votes.
Rory Daulton Rory Daulton Does this mean I'll only consider the part from 0, y up to point B? The problem only considers the two ships at the two times noon and pm, and my diagram covers the two ships at the two times.
There is no need to consider other times or places. David K David K As long as all the formulas you finally use are based on the new axes which they are, of course, in your answer then all is fine. David Quinn David Quinn Thanks for that, edited accordingly. I hope we are now in agreement. I hesitated about entering an answer when I saw your perfectly-formed offering, but I was half-way through typing it, somewhat laboriously, so I decided to persevere I think your work here is good.
Plus, you continued to the final answer, which I decided not to do since the OP did not ask for it. I removed the negative sign in front of the final answer, since it seems that you meant to do that. I hope you don't mind. Put it back if you want it there. I though I removed it myself! Thanks anyway.
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