Category:Definitions/Tangents
This category contains definitions related to Tangents.
Related results can be found in Category:Tangents.
Let $f: \R \to \R$ be a real function.
Let the graph of $f$ be depicted on a Cartesian plane.
Let $A = \tuple {x, \map f x}$ be a point on $G$.
The tangent to $f$ at $A$ is defined as:
- $\ds \lim_{h \mathop \to 0} \frac {\map f {x + h} - \map f x} h$
Thus the tangent to $f$ at $x$ can be considered as the secant $AB$ to $G$ where:
- $B = \tuple {x + h, \map f {x + h} }$
as $B$ gets closer and closer to $A$.
By taking $h$ smaller and smaller, the secant approaches more and more closely the tangent to $G$ at $A$.
Hence the tangent to $f$ is a straight line which intersects the graph of $f$ locally at a single point.
Also see
Subcategories
This category has the following 3 subcategories, out of 3 total.
Pages in category "Definitions/Tangents"
The following 8 pages are in this category, out of 8 total.