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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.
Cylinder The below equation is the common equation of a cylinder. x 2 /a 2 + y 2 /b 2 = 1 This is known as a cylinder whose cross section is an ellipse. If a = b we
The angle calculate of the base angles of an isosceles triangle are shown by x and the vertex angle is 3x + 10. Determine the measure of a base angle. a. 112° b. 42.5° c.
Determine or find out the area of the inner loop of r = 2 + 4 cosθ. Solution We can graphed this function back while we first started looking at polar coordinates. For thi
Note that there are two possible forms for the third property. Usually which form you use is based upon the form you want the answer to be in. Note as well that several of these
Need help, Determine the points of inflection on the curve of the function y = x 3
Children of the same age can be at different operational stages, and children of different ages, can be at the same developmental stage." Do you agree with this statement? If so, g
1+1
In the earlier section we modeled a population depends on the assumption that the growth rate would be a constant. Though, in reality it doesn't make much sense. Obviously a popula
Determine or find out the direction cosines and direction angles for a = (2, 1, -4) Solution We will require the magnitude of the vector. ||a|| = √ (4+1+16) = √ (21)
briefly explain how the famous equation for the loss of heat in a cylindrical pipe is derived
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