(a)Express f in standard form
(b)Find the vertex and x- and y-intercepts of f.
(c)Sketch the graph.
(d)Find the domain and range of f.
On comparing it with equation (1) we get:
So, we have (0,3) as the y−intercept.
Now the x−intercept is given by equating
Proving single solution to an initial value problem
or each I need to prove that there is a single solution defined on
Can this ODE system be solved?
Is there a method to solve the following ODE system?
with initial conditions .
Verify that the function is a solution to the differential equation
is a particular solution to the differential equation:
I will verify this by differentiating the function with respect to t.
I'm having trouble solving the integral because it involves an error function. Could I get some pointers on how to evaluate this? Or is there a different way to verify that the function is a solution?
Showing that continuous and differentiable s(t), with and for , is identically zero for .
Let be a continuous function that is differentiable on .
It also holds that
Show that .
Do we us some theorem, maybe Rolle or the mean value theorem?
Do we have to check maybe the sign of ? This depends on the value of s(t), or not?
Finding a constant such that the following integral inequality holds:
Constant: such that for all function in