Recent content by sergey90

Homework Statement #1. If limit[x->a]f(x) exists, but limit[x->a]g(x) doesnt, limit[x->a](f(x)+g(x)) doesn't exist. T/F? (Proof or example please) #2. prove that if f is continuous, then so is |f| #3. f(x) = [[x]]+[[-x]] for what a does limit[x->a]f(x) exist? Where is f discontinuous...

Homework Statement f(x)= xsin(1/x) if x!=0 = 0 if x=0 does the derivative exist at x=0? Can somebody please provide a visual backup of the result? Is this supposed to be a cusp that's why there is no derivative on a continuous function? Homework Equations The Attempt at a...

its the epsilon delta proof for infinite limits. Its just how they are proved generally. M is any negative number

Homework Statement limit[1/(x-2)^3]=-inf as x->2 Homework Equations The Attempt at a Solution 2-delta<x<2 1/(x-2)^3 < M -delta<x-2<0 (x-2)^3>1/M (-delta)^3<(x-2)^3<0 =>(-delta)^3=1/M=>-delta=croot(1/M)=>delta=-croot(1/M) ...huh? how could delta be...

Hi guys, just embarking on the journey of modeling with differential equations and solving them. I have a more conceptual quesiton. Linear differential equations in my book are defined to be ones where F(t, y, y', y'',...,yn) = 0 is a linear function of the dependent var y and all of its...

so i could just equate the dimension of pressure to a dimensional relationship involving gravitational acceleration, Volume of the water, and the area of the water and still get the dimensions of pressure,without involving the depth z. But this doesn't make sense, since we all know depth does...

oh i forgot to say that one solution i came up with was with scaling. I would just say "if x=1 then w is 0. if x=2 then w=-1 and the relationship holds for all value. Thus we just pick x to be 1 and regard mass as unimportant for pressure. Is this a correct way to go about this? Im assuming not...

Homework Statement Pressure(water)~density(water)xg(grav. accel.)xz(depth) Homework Equations The Attempt at a Solution basically I'm doing a fermi problem regarding the pressure of water on Jupiter's moon Europa. Now i tried coming up with the equation for pressure my self by...

thanks for the help guys. One last clarification on the matter: in previous problems of fractional errors if for example we have a value of 9.69+-0.07cm^2 the book just divides 0.07 by 9.69 and says that's my fractional error % without multiplying by 100. Why so?

Homework Statement Estimate the percent error in measuring a distance of about 75cm with a meter stick. Homework Equations The Attempt at a Solution I'm assuming one could accurately measure this value to a couple mm. so it would be 75+-0.2cm. Now the book gives an answer of...