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Tangent, Normal and Binormal Vectors
In this part we want to look at an application of derivatives for vector functions. In fact, there are a couple of applications, but they all come back to requiring the first one.
In the past we have employed the fact that the derivative of a function was the slope of the tangent line. Along with vector functions we obtain exactly similar result, along with single exception.
There is a vector function, r→ (t) , we call →r′ (t) the tangent vector specified by it exists and provided →r′ (t) ≠ 0 . After that the tangent line to →r (t) at P is the line that passes via the point P and is parallel to the tangent vector, →r′ (t).
Notice: we really do need to require r?′ (t) ≠ 0 to have a tangent vector. Whether we had →r′(t) = 0→ we would have a vector that had no magnitude and thus could not give us the direction of the tangent.
Derivatives to Physical Systems: A stone is dropped into a quiet lake, & waves move within circles outward from the location of the splash at a constant velocity of 0.5 feet p
the first question should be done using the website given (www.desmos.com/calculator )and another good example to explain using the graph ( https://www.desmos.com/calculator/ydimzr
Find the slope of the line tangent to the graph of f(x)= 3-2ln(2x^2+4) at the point (4, F(4))
Power Series and Functions We opened the previous section by saying that we were going to start thinking about applications of series and after that promptly spent the section
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round 64 to the nearest 10
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