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The formula simplifies: = ′ (). The unit tangent vector determines the orientation of the curve, or the forward direction, corresponding to the increasing values of the parameter. The unit tangent vector taken as a curve traces the spherical image of the original curve.
The higher order derivatives can be applied in physics; for example, while the first derivative of the position of a moving object with respect to time is the object's velocity, how the position changes as time advances, the second derivative is the object's acceleration, how the velocity changes as time advances.
If the boundary of Ω is C k for k ≥ 2 (see Differentiability classes) then d is C k on points sufficiently close to the boundary of Ω. [3] In particular, on the boundary f satisfies = (), where N is the inward normal vector field. The signed distance function is thus a differentiable extension of the normal vector field.
In physics this theorem is one of the ways of defining a conservative force. By placing φ as potential, ∇ φ is a conservative field . Work done by conservative forces does not depend on the path followed by the object, but only the end points, as the above equation shows.
In complex analysis, complex-differentiability is defined using the same definition as single-variable real functions. This is allowed by the possibility of dividing complex numbers . So, a function f : C → C {\textstyle f:\mathbb {C} \to \mathbb {C} } is said to be differentiable at x = a {\textstyle x=a} when
A man was left in critical but stable condition after he was pushed onto the subway tracks at the 18th Street station in Manhattan's Chelsea neighborhood. The 45 -year-old victim was pushed onto ...
3. Plan your withdrawal strategy. Most retirement strategies plan for saving, not spending. So it’s not always easy to remember that there will come a time you have to spend the money you’ve ...
'Tis the season for getting cozy. If you're anything like me, curling up on the couch with all things soft and warm sounds like a perfect night.