**Preface**

This series is aimed at providing tools for an electrical engineer to analyze data and solve problems in design. The focus is on applying calculus to equations or physical systems.

**Introduction**

This article will introduce limits.

There are many calculus references, the one I like to use is Calculus by Larson, Edwards and Hostetler.

This also assumes you are familiar with Python or can stumble your way through it.

**Concepts***Limit: *the value a function approaches as it gets close to a given set of input coordinates.*Asymptote: *if as x approaches infinity f(x) approaches a constant value c.

**Formal Definition of a Limit**

Let f be a function and let c and L be real numbers. The limit of *f(x)* as x approaches c is L iff:

lim_{x->c-}=L and lim_{x->c+}=L (i.e. from the left and from the right).

**Definition of Continuity**

A function f is continuous at c if the following three conditions are met:

- f(c) is defined
- lim
_{x->c}f(x) exists - lim
_{x->c}= f(c)

Functions can also be open on an interval or everywhere continuous (infinite).

**Properties of Limits**

General Form | lim_{s->c} f(x)=L; lim_{s->c} g(x)=K |

Constant | lim_{x->c} b=b |

Variable | lim_{x->c} x=c |

Scalar Power | lim_{x->c} x^{n}=c^{n} |

Scalar Multiple | lim_{x->c} b*f(x)=b*L |

Sum/Difference | lim_{x->c} [f(x) +/- g(x)]=L +/- K |

Product | lim_{x->c} f(x)*g(x)=L*K |

Quotient | lim_{x->c} f(x)/g(x)=L/K; providing K != 0 |

Power | lim_{x->c} f(x)^{n}=L^{n} |

Radical | lim_{x->c} rad_{n}(f(x))=rad_{n}(L) |

Where b, c, n, L and K are constants, x is a variable and *providing the limit exists*.

**Next Up**

Differientiation

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