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Originally posted by: Miggi

Which of the following clusters of orbitals would form the shape shown here (Part C 1 figure) and would also be possible within the valence shell of an atom?

Check all that apply.

three p orbitals two sp orbitals and four p orbitals three sp orbitals two sp orbitals and two p orbitals six sp^3d orbitals six sp^3d^2 orbitals correct six sp^3 orbitals one sp orbital and two p orbitals

figure:

Originally posted by: Miggi

Use differentials (or, equivalently, a linear approximation) to estimate the given number.

sqrt100.4

I got 10.02 is it right?

Originally posted by: Miggi

Find the critical numbers of the function.

f(x)= x^-2lnx

I am not sure but i got e^2 and 0. Not sure which one is correct. can ny1 help?

Originally posted by: akhl

f(x) = x^-2 * lnx

f ' (x) = x^-2 * d/dx (lnx) + d/dx (x^-2) * lnx

= x^-2 * 1/x + (-2) x^-3 * lnx

= x^-3 - 2 x^-3 lnx

= x^-3 (1 - 2 lnx)

For critical points, f ' (x) = 0

Therefore x = 0, 1-2lnx = 0

x = 0, lnx = 1/2

x = 0, sqrt(e)

Note: sqrt = square root.

Ans: x = 0, sqrt(e)