<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>