Homework Statement
Find the values of a and b that make f a differentiable function.
Note: F(x) is a piecewise function
f(x):
Ax^2 - Bx, X ≤ 1
Alnx + B, X > 1
Homework Equations
The Attempt at a Solution
Made the two equations equal each other.
Ax^2 - Bx = Alnx + B
Inserting x=1 gives,
A -...
Consider the function:
$$F(s) =\begin{cases} A \exp(-as) &\text{ if }0\le s\le s_c \text{ and}\\
B \exp(-bs) &\text{ if } s>s_c
\end{cases}$$
The parameter s_c is chosen such that the function is continuous on [0,Inf).
I'm trying to come up with a (unique, not piecewise) Maclaurin series...
Homework Statement
Write F(x)= x2-5|x| as a piecewise function
Homework Equations
The Attempt at a Solution
I was writting it out and came to
Fx= x2-5(x) and x2-5(-x)
but my book says that it comes out to be
x2-5
x2-5(-x)
I imagine there is a very simple reason why the x in the first one...
Okay, so I'm down to the last equation.
-12/11 x 10 + 54/11 I get -66/-99. Is this right? If so how do I put it into the graph.
-12/11 x 10 = -120/110 + 54/11 = -66/99 (I think I've went wrong somewhere)
I recently plotted a piecewise function:
Plot[Piecewise[{{1 - Exp[-.002*t],
0 <= t < 120}, {-Exp[-.002*t] + Exp[-.002*(t - 120)],
120 <= t}}], {t, 0, 5000}, PlotRange -> {0, 0.25}]
I then defined the function which I am calling q[t_] as follows:
q[t_] := Piecewise[{{1 -...
Homework Statement
I've entered the following piecewise equation into Mathematica:
Plot[Piecewise[{{sin (t), 0 <= t < \[Pi]}, {5 + 5 cos (t) + sin (t), \[Pi] <= t < 4*\[Pi]}, {10 cos (t) + sin (t), 4*\[Pi] <= t}}], {t, 0, 20*\[Pi]}]
But I am getting a blank graph in return. I've proofread my...
Homework Statement
f(x)=-2 when x<1
=3 when x=1
=x-3 when x>1
find the limit at 1 from the left and right sides and at 1.
Homework Equations
The Attempt at a Solution
limit for x when approaching 1 from the left is -2
limit for x when approaching 1 from the right is -2
-I'm not...
1. Problem
Define a function:
for t>=0, f(x,t) = { x for 0 <= x <= sqrt(t), -x + 2sqrt(t) for sqrt(t) <= x <= 2sqrt(t), 0 elsewhere}
for t<0 f(x,t) = - f(x,|t|)
Show that f is continuous in R^2. Show that f_t (x, 0) = 0 for all x.
Then define g(t) = integral[f(x,t)dx] from -1 to 1. Show...
Dear Friends
I have a question about linear programming. It would be great to have your comments or suggestions.
Consider the followings
\begin{equation}
\\
Y = [y_{1}, y_{2}, \cdots, y_{n}]
\\
G = [g_{1}, g_{2}, \cdots, g_{n}]
\\
\textbf{X} =
\begin{pmatrix}
0 & x_{1,2} & \cdots & x_{1,n}...
Homework Statement
Homework Equations
The Attempt at a Solution
Not sure what to do here. I was thinking maybe the y – y1 = m(x – x1)? I am having trouble understanding this question. I know what piecewise functions are but filling this in is proving difficult.