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- StudyBlue
- North-carolina
- University of North Carolina - Charlotte
- Calculus
- Calculus 1242
- Birdsong
- Calc 3 10.7-11.1

Gabe R.

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51
vector-valued function or vector function

a function whose domain is a set of real numbers and range is a set of vectors

component functions

functions within a vector function.

ex) r(t) = <f(t), g(t), h(t)>

Limit of a vector function

is the limit of it's component functions

lim r(t)

t->a

<lim f(t), lim g(t), lim h(t)> as t->a

When is a vector function r continuous at a?

when the

lim r(t) = r(a)

t->a

space curve

The set of C of all points (x,y,z) in space, where t varies through out the interval I. ( the graph of a vector function in space

x=1+t

y=2=5t

z=-1+6t

these are examples of what?

x=1+t

y=2=5t

z=-1+6t

what is the parameter of these eqs?

How is a space curve traced?

what shape do these parametric eqs form?

x=cost

y=sint

z=t

2 equations of a circle?

Definition of derivative of vector function

what is tangent vector to r(t)?

Tangent line to curve C at P

unit tangent vector

Theorem 4

(derivatives)

if r(t)=<f(t), g(t), h(t)>=<f(t)i+g(t)j+k(t)k>

1) vector derivative rule

d/dt [u(t)+v(t)]

2nd derivative rule d/dt [cu(t)]

3rd derivative rule

d/dt [f(t)u(t)]

4th derivative rule d/dt [u(t)*v(t)]

5th derivative rule d/dt [ u(t) X v(t)]

6th derivative rule d/dt [u(f(t))]

definite integral of vector function

Fundamental Theorem of Calculus

General formula for arc length

when is a parameterization called smooth?

The formula for curvature is?

Theorem 10) The curvature of the curve of a vector function

||T'||/||r'|| is equal to what?

for special case of a plane curve with equation y=f(x)

principal unit normal vector N(t) is also known as?

N(t) unit normal

Binormal vector

B(t)

Normal Plane

Osculating Plane

Circle of curvature

Velocity Vector

speed of a particle at time t

acceleration

Newton's Second law of motion

Centripetal Force

Parametric Equations of trajectory

Acceleration

a_{n}

Kepler's first law

Kepler's 2nd law

Kepler's 3rd law

Law of Gravitation

a function of two variables

Level Curve

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