Recent content by newyorkcity

i honestly don't have a clue. the only thing relevant i can think of is that a more highly substituted carbon atom will form a more stable radical / carbocation. I'm not sure what this might imply in this situation, if anything. ..?

why is t-butoxide a stronger base than ethoxide?

I think I figured this out. So I think the -#-yl (when used with bicyclo subunits) denotes the carbon on the subunit that attaches to the main compound. In the case presented above, the bicyclo[2,1,0]pentyl is not attached via a bridgehead C but rather one C over, but since the 'cyclopropyl'...

Hi all, I have a question regarding the nomenclature of organic compounds. What is the significance of -5-yl in bicyclo[2,1,0]pent-5-ylbicyclo[3,3,0]octane ? In general, what is the significance of the # in -#-yl in compounds? Additionally, in (E)-1,2-diiodo-1methylcyclohexane, does the E...

See the post immediately above this one. Are you just implying that I should use linear algebra, subtracting / adding equations to find the transformation funcs as functions of u,v?

No problem, I am sure that information might be of use to someone who comes across this thread in the future. So what I have pulled together is the following... Using lin alg to convert the transformation functions: x=u/3 + v/3 y=2u/3 - v/3 J = |d(x,y)/d(u,v)|= |1/3 1/3| |2/3 -1/3|...

I think I understand that already, see above... my problem was that I copied the functions, on paper, in terms of y so that I could plot the functions. I overlooked the relationship because of this (whoops, really tired lol).

I understand that the Jacobian is the determinant. What this means to me is that I should find: | du/dx du/dy | | | | dv/dx dv/dy | From what I understand, the Jacobian of the transformation given by x=g(u,v) and y=g(u,v) is: |d(x,y) / d(u,v)| But because my...

The general formula for the Jacobian is |d(x,y) / d(u,v)|... so in this case, would I find |d(u,v) / d(x,y)|, since I can't find the first unless the transformation functions are not in terms of u and v? Just to confirm, after finding the Jacobian, to find the area, I will compute: int(...

The problem is: R is the parallelogram bounded by the lines x+y=2, x+y=4, 2x-y=1, and 2x-y=4. Use the transformation u=x+y and v=2x-y to find the area of R. I am not sure how to complete this problem. My first issue is that I don't know how to convert the transformation functions into...

How would I analyze the continuity of: g(x,y) = sin(2x^2 - y^2) / 2x^2-y^2 unless y^2=2x^2 1 if y^2=2x^2 g(x,y) seems to be continuous for all values of (x,y)... However, I realize that the function assumes the value 0 when y^2=2x^2. I am not really sure how to go further than this... the...

Looking back at the text, I just missed the relationship between (a,b), (x0,y0), and (x,y). To clarify, the 'Tangent Plane' equation is used to find the tangent plane at a point P(x0,y0,z0). The 'Linearization' equation yields the linear approximation of f(x,y) at (a,b). Thanks for your help.

What is the difference? According to my text... Tangent Plane: z-z0=fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0) Linearization: L(x,y) = f(a,b) + fx(a,b)(x-a) + fy(a,b)(y-b)

What is the difference? According to my text... Tangent Plane: z-z0=fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0) Linearization: L(x,y) = f(a,b) + fx(a,b)(x-a) + fy(a,b)(y-b)

Homework Statement Find all second partial derivatives of z=arctan((x+y)/(1-xy))Homework Equations d/dx of arctan(x) is 1/(1+x^2)The Attempt at a Solution Not sure how to proceed... I don't want the answer, just an idea as to how to move forward. My attempt at finding the first...