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### Transforming Piecewise Functions

Homework Statement The piece wise function is -x-2, x<-1 x^2-3x, -1≤ x ≤5 3x+5, x>5 The problem is to transform the function with...
2. ### Find A and B so that F(x) is a Differentiable Function

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 -...
3. ### A Taylor/Maclaurin series for piecewise defined function

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...
4. ### Absolute function into piecewise function

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...
5. ### -66 over -99 into a graph?

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)
6. ### Mathematica FindMaximum function in Mathematica

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 -...
7. ### Mathematica Mathematica not plotting

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...
8. ### Finding limits to a piecewise function (3 pieces)

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...
9. ### Multivariate piecewise fxn continuity and partial derivative

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...
10. ### Piecewise linear programming

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}...
11. ### Filling in piecewise function from given graph

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.