Recent content by kolua

so there is no such relationship and I should disprove statement?

by reflection?

no, i don't think there fixed pionts should be taken into consideration. should they?

Homework Statement Prove or disprove: Every translation is a product of two non-involutory rotations. Homework EquationsThe Attempt at a Solution :[/B] I am not sure if I got the right proof for the special situation: A translation is the product of two reflections with parallel reflections...

Yes, I know how to prove the third condition. ai=b-1/n as a goes to infinity. But what about the second condition? how should I prove that Ac is an event? Ac=[b, infinity)

Homework Statement Suppose that the sample space is the set of all real numbers and that every interval of the form (-infinity, b] for any real number b is an event. Show that for any real number b (-infinity, b) must also be an event. The Attempt at a Solution use the 3 conditions required...

I'm not sure if the graph looks like that. Because the calculator gives a different image.

x approaches infinity and function goes to pi/4 that's the definition of a horizontal asymptote, correct?

is the horizontal asymptote correct? is there any other horizontal asymptote that I am missing? I got a graph like this, but I'm not sure if it is correct

when x=-1 arctan is undefined but as x approaches x=-1 (x-1)/(x+1) approaches negative infinity and positive infinity from left and right. Let (x-1)/(x+1) = t, then arctan(t) approaches pi/2 and -pi/2 as t approaches the two infinity is this correct? then there is no vertical asymptote?

I think the limit of arctan((x-1)/(x+1)) as x approaches -1 from the right is pi/2 and as x approaches -1 from the left is -pi/2, which means there is no vertical asymptote here but a jump discontinuity here right?

I am so far able to find the domain, intercepts, concavity and increase/decrease. But I am stuck at finding the asymptotes for the graph. I think there is no vertical asymptote or is there one at x=-1? I think the horizontal asymptote is y=pi/4

I got 0.316 and the answer is 3.16. thanks, I think I might have made mistake in the decimal.

Homework Statement A sample containing 3.65 mol of a monatomic ideal gas is heated from 289K to 458K, and the entropy remains constant. If the initial volume of the sample was 0.0980m^2, by what factor did the pressure increase or decrease during this process? Homework EquationsThe Attempt at...

Homework Statement Two moles of an ideal gas undergo a reversible isothermal expansion from 3.37×10−2m3 to 4.29×10−2m3 at a temperature of 29.6 ∘C. What is the change in entropy ΔS of the gas? Homework Equations pV=nRT The Attempt at a Solution W=∫V2V1pdV, I don't know how to use this...