How many electrons does the HOMO of 1, 3-pentadiene have in its excited state?

What is an appropriate stepwise synthesis to carry out the conversion shown?

Identify the structure of the product from the the following reaction sequence.

Find the absolute extreme values of the function on the interval.f(x) = ln(x + 2) + , 1 ≤ x ≤ 10

Find the slope of the curve at the given point P and an equation of the tangent line at P.y = x3 – 9x, P(1, -8)

Find the most general antiderivative. dx

Determine whether Rolle’s Theorem applies to the following functions on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle’s Theorem.f(x) = cos 10x; 

Write the function in the form y = f(u) and u = g(x). Then find dy/dx as a function of x.y = cot(7x – 4)

Find the second derivative of the function.y = 

A niche is a(n) ______.