Examples For How to Find Smooth Intervals of Vector-Valued Functions (Calculus 3)
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In this video we look at examples of using the derivative of a vector function to find intervals where it is smooth (for both plane and space curves).
This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Example 1: 〈3t^2-2, 2t^3-6t〉
4:56 Example 2: 〈1/(t-1), 3t〉
10:56 Example 3: 〈2cos^3(t), 3sin^3(t)〉, 0 ≤ t ≤ 2π
20:10 Example 4: 〈(t-1), 1/t, -t^2〉
25:55 Example 5: 〈e^t, -e^(-t), 3t〉
29:32 Example 6: 〈√t, (t^2-1), t/4〉
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