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A patient who has rheumatoid arthritis (RA) has been taking methotrexate for 6 months and OTC NSAIDs as needed for pain. The patient reports that symptoms seem to be getting worse. The provider refers the patient back to the rheumatologist and expects the rheumatologist to:

Rank the following dienophile in order of increasing reactivity in a Diels-Alder reaction, listing the least reactive first.  

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

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; 

Find the most general antiderivative. dx

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)