- #1

- 96

- 0

## Homework Statement

In calculus II, vector valued function in space. The vector function

**r**(t)=f(t)

**i**+g(t)

**j**+h(t)

**k**. The curve traced by

**r**is smooth if d

**r**/dt is continuous and NEVER

**0**.

## Homework Equations

I don't understand why there is "NEVER 0" in the above statement, in order for the curve traced to be smooth.

## The Attempt at a Solution

The original statement appear in texts such as Thomas/Finney Calculus, Davis (introduction to vector analysis). But their explanations are very different. In learning calculus I, a smooth curve does not seem to require dy/dx=0 (e.g. y=x^3 is a smooth everywhere). Why in dealthing with vector calculus, there is such restriction.

Thanks