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Surfaces.
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Curves in the plane
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Limits and Continuity.
Derivatives.
Definition 2.11
The function
is differentiable at
t
_{0}
if there exists a vector
such that
We denote:
Proposition 2.12
The function
is differentiable at
t
_{0}
if, and only if each component
f
_{i}
is differentiable at
t
_{0}
. We have:
Example 2.13
If
, then
.
Definition 2.14
With the notations of refdef derivation. Let the function
describe the motion of a particle.
1.
The vector
is the
velocity vector
of the particle at time
t
_{0}
.
2.
The number
is the
speed
of the particle at
t
_{0}
.
Definition 2.15
With the same notations. The
acceleration
at
t
_{0}
is the derivative of
at
t
_{0}
. we denote it by
.
Example 2.16
Let
. Then:
Velocity:
.
Acceleration:
.
Please check that, in this example,
are orthogonal for every value of
t
.
Noah Dana-Picard
2001-05-30