Help me with these calculus questions!!!

Test Preparation
1

<li>Let f be the function given by f(x)=(ax+b)/((x^2)-c) and that has the following properties:
(i) the graph of f is symmetric with respect to the y-axis.
(ii) lim f(x)=+infinity
x->2+
(iii) f’(1)=-2 , here it is derivative of f(x) at 1</li>
</ol>

<p>(a) determing the values of a, b, and c
(b) write the equation for each vertical and each horizontal asymptote of the graph of f</p>

<li>a particle moves along the y-axis so thnat its velocity at t greater than or equal to 0 is given by v(t)=1-arctan(e^t). At time t=0, the particle is at
y=-1.
(a) find the acceleration of the particle at time=2
(b) is the speed of the particle increasing or decreasing at time t=2? Why
(c) find the time t greater than or equal to 0 at which the particle reaches
its highest point. Why?</li>
</ol>

2

<p>1(a).
(i)
Symmetry with respect to the y-axis =>
f(x) is even and formula f(x)=P(x)/Q(x), where P(x) and Q(x) are polynoms,
should not include x^n with odd n => a=0.
Or: for even functions f(x) = f(-x) => ax=0 for any x => a=0.</p>

<p>f(x) = b/(x^2-c)</p>

<p>(ii)
lim f(x)=+infinity for x->2+ => lim(x^2-c)=0 => c=2^2=4
f(x) = b/(x^2-4)</p>

<p>(iii)
f'(x) = -2bx/(x^2-4)^2
f'(1) = -2 => -2b/9=-2 => b=9 </p>

<p>f(x) = 9/(x^2-4)</p>

<p>1(b).
Vertical asymptots x=2 and x=-2, horizontal y=0.
+++++++++++++</p>

<p>2.
Should read </p>

3

<p>I just noticed that the second part of my post was cut off.
It started:
"Should read
At time t=0, the particle is at y=1."</p>

<p>kevin4242 - if it's still needed I'll post my lost answer later.</p>

4

<p>looks like someone is doing the old ab calc problems assigned for hw lol. i remember practicing those, theyre like 1988 right?</p>