Hi to all. I have a piecewise function and I want to differentiate it but the derivative will not exist at endpoints. I tried to interpolate it such that the edges are more smooth and the derivative is continuous, but when I plot it, I still get the harsh edges. What to do now? Th...
I need to plot the two piecewisely defined functions on the same graph. Please help me to write code. Thanks in advance. f(x)= 1-sqrt{5-x} for x =<5, 1 for 5=< x =<7, 1-sqrt{(x-7)/3} for x =>7. Similarly, g(x)= sqrt{(5-x)/2} for x =<5, 0 for 5=...
How to Graph a Piecewise-defined Function: F(x) = a for Each Defined Region of X: Example 2 {eq}f(x)=\begin{cases} 1, & \text{if} -3< x \leq -2 \\ -2, & \text{if } -2 < x \leq 1 \\ 2, & \text{if} 1< x \leq 2 \end{cases} {/eq}...
This technique is very general: it works for a broad class of approximating functions, including piecewise polynomials; it can be applied to both Bellman and Euler equations; and it is compatible with both continuous﹕tate and discrete﹕tate shocks. In the case of normally distributed shocks, ...
The function |x| gives the magnitude of the variable irrespective of the direction. In other words, |x| returns x if x≥0 and −x if x<0. It is represented as the following piecewise function: |x|={−x, if x<0x, if x≥0...
Determine whether the equation represents v as a function of x. x2 + y2 = 4 Test for exactness and solve 6 x^5 y^3 + 4 x^3 y^5 dx + 3 x^6 y^2 + 5x^4 y^4 dy = 0 How to determine if f^x is a quadratic residue?
Several pages of algebra are required to solve for the upper and lower sums of even the simplest polynomial function—, like y = 3x2. if you want to use algebra, follow the (very lengthy) explanation that Stan Brown provides on his article “Area by Upper and Lower Sums.” You can ...
It is a very simple example that I ask you to tell me to understand the syntaxes. I think that is easy for you, ;-) writen in a single line, please. (this example is easy to implement with "piecewise function", the problem is that, in my piecewise function, the ranges depend o...
Step 1:This is a piecewise function with a removable discontinuity at {eq}x=0, x=3 {/eq}, and {eq}x=5 {/eq} . Although we have a multiple removable discontinuities, we can still calculate the definite integral like in the previous two examples. Although the entire f...
How to Solve LimitsThe following techniques apply to limits of the form \lim _{x \rightarrow a} F(x) \\where F is a function which is at least continuous for x near a, but maybe not at x = a itself.…