# Category:Tangents

This category contains results about **Tangents**.

Definitions specific to this category can be found in Definitions/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 11 subcategories, out of 11 total.

### A

- Angles of Contingence (empty)

### B

- Bitangents (empty)

### C

- Chords of Contact (2 P)
- Common Tangents (1 P)

### D

- Double Tangents (empty)

### P

### T

- Tangent Planes (empty)
- Tangent Secant Theorem (4 P)
- Tangent-Chord Theorem (3 P)
- Tangents to Circles (9 P)

## Pages in category "Tangents"

The following 7 pages are in this category, out of 7 total.