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a) The limit of the position of particle when time approaches 2 is
.
b) The velocity of particle is
for all
.
c) The rate of change of the distance between particle and particle
at time
is
.
a) To determine the limit for , we need to apply the following two <em>algebraic</em> substitutions:
(1)
(2)
Then, the limit is written as follows:
The limit of the position of particle when time approaches 2 is
.
b) The function velocity of particle is determined by the <em>derivative</em> formula for the division between two functions, that is:
(3)
Where:
- Function numerator.
- Function denominator.
- First derivative of the function numerator.
- First derivative of the function denominator.
If we know that ,
,
and
, then the function velocity of the particle is:
The velocity of particle is
for all
.
c) The vector <em>rate of change</em> of the distance between particle P and particle Q () is equal to the <em>vectorial</em> difference between respective vectors <em>velocity</em>:
(4)
Where is the vector <em>velocity</em> of particle P.
If we know that ,
and
, then the vector rate of change of the distance between the two particles:
The magnitude of the vector <em>rate of change</em> is determined by Pythagorean theorem:
The rate of change of the distance between particle and particle
at time
is
.
<h3>Remark</h3>
The statement is incomplete and poorly formatted. Correct form is shown below:
<em>Particle </em><em> moves along the y-axis so that its position at time </em>
<em> is given by </em>
<em> for all times </em>
<em>. A second particle, </em>
<em>, moves along the x-axis so that its position at time </em>
<em> is given by </em>
<em> for all times </em>
<em>. </em>
<em />
<em>a)</em><em> As times approaches 2, what is the limit of the position of particle </em><em> Show the work that leads to your answer. </em>
<em />
<em>b) </em><em>Show that the velocity of particle </em><em> is given by </em>
<em>.</em>
<em />
<em>c)</em><em> Find the rate of change of the distance between particle </em><em> and particle </em>
<em> at time </em>
<em>. Show the work that leads to your answer.</em>
To learn more on derivatives, we kindly invite to check this verified question: brainly.com/question/2788760