Unformatted text preview: and this vector varies continuously with x . Also, since its Frst component is always 1, it is always a nonzero vector: we express this by saying that −→ p ( x ) has nonvanishing velocity . 3. At each point P ( x ,f ( x )) on the curve, gr ( f ) has a tangent line : this is the line through P with slope dy dx = f ′ ( x ) . The velocity vector −→ v ( x ) points along this line, so it can be used as a direction vector for the tangent line. 13 Although in principle only diferentiability is needed, we also assume the derivative is continuous; dealing with examples oF Functions with possibly discontinuous derivatives could distract us From our main goal here. 14 A synonym For one-to-one, derived From the ±rench literature, is injective ....
View Full Document
This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08