Piece-wise function Definition and 16 Threads

For this, , The solution is, However, should they not write ##f(x) = \cos x## on ##[\frac{pi}{4}, \infty)## Many thanks!

The implicit curve in question is ##y=\operatorname{arccoth}\left(\sec\left(x\right)+xy\right)##; a portion of the equations graph can be seen below: In particular, I'm interested in the area bound by the curve, the ##x##-axis and the ##y##-axis. As such, we can restrict the domain to ##[0...

help me please to determine what are the equations i need tofinish my activity. Thankyou

image due to macros in Overleaf ok I think (a) could just be done by observation by just adding up obvious areas but (b) and (c) are a litte ? sorry had to post this before the lab closes

I have been working on this exercise 5 and kind of stuck how to start the problems. I would think to start with a graph, but I feel this is wrong. I am just stuck on a and b.

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 http://s23.postimg.org/wsj9e91wb/IMG_1334.jpg[/B] photo of the problem g(x)=∫ƒ(t) dt from -5 to x ƒ(t) = (0 if x < -5 5 if -5≤x<-1 -3 if -1≤≤x<3 0 if x≥3) (a) g(-8) = 0 (b) g(-4) = 5 (c) g(0) = ? (d) g(4) = ? Homework Equations ∫ƒ(x) from...

The function is g(x) = (x^2 - a^2)/(x - a) if x doesn't equal a; and the second part is g(x) = 8 when x = a. The question asks for me to find a specific value for a so that the function might be continuous on the entire real line. I know that each part of the piece-wise function needs to...

f: Z -> Z defined by f(x) = x/2 if x is even, (x-1)/2 if x is odd. Proof: If x is even: x1 = 2k1 x2 = 2k2 Suppose f(x1) = f(x2), then 2k1/2 = 2k2/2 k1 = k2 So if x is even, the function is one to one? Is this an okay proof for the first half of if x is even, then I just do the...

1. Suppose f(x)=0 if x is irrational, and f(x)=x if x is rational. Is f differentiable at x=0? 2. the derivative= lim[h->0] [f(a+h)-f(a)]/h 3. I don't really know how to start, but I do know that between any two real numbers, there exists a rational and irrational number. So I'm...

Homework Statement Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. f(x)= {x^3 if x < or = -2 {2 if x > -2 Homework Equations The conditions are that a function is said to be...

Homework Statement Function f and g are defined as follows : f(R)=R , f(x)=x^2 , g(R)=R , g(x)=x+1,x>=0 , -x , x<0 (its a piecewise function) . Find fg(x) and gf(x) . Homework Equations The Attempt at a Solution fg(x)= (x+1)^2 , x>=0 x^2 , x<0 gf(x)= x^2+1 , x>=0...

[SOLVED] Continuity on a piece-wise function Problem: Suppose: f(x)=\left\{\begin{array}{cc}x^2, & x\in\mathbb{Q} \\ -x^2, & x\in\mathbb{R}\setminus\mathbb{Q}\end{array}\right At what points is f continuous? Relevant Questions: This is in a classical analysis course, not a...

I am doing my calculus homework and two problems are holding me up. The first says: Using one-sided derivatives, show that the function f(x) = x^3, x_<_1 3x, x>1 does not have a derivative at x=1 Now it is painfully obvious that the function is not continuous at x=1. however, i...

I'm doing a review of fuctions, and a nagging question popped up in my mind after completing this problem. After graphing y = |x| + x, express this equation as a piece-wise function with no absolute values. I did graph it; it was simple (following is a sketch without values)...