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Each line below is a step in the process of using the limit definition of derivative to determine the formula for \(f\,^\prime(x)\) when \(f(x)=x^2+1\). Put the steps in the correct order.

The population of chipmunks at a nature preserve is modelled by the function \(P(t)=\dfrac{`a`0}{1+7e^{-0.035t}}+`b`0\) adult chipmunks, where \(t\) measures the time, in months, since chipmunk monitoring began at the site. What does this model predict for the maximum number of chipmunks at the preserve?   Desmos (click to reveal)

If \(f(x)=3x^2-x+1\), which of the following is a correct expression for \(f(x+h)\)?

The metabolism of a \(t\)-day-old albatross chick is given by \(m(t)\) watts per kilogram (\(\tfrac{W}{kg}\)).  \(m\,^\prime(10)=2\) means that when an albatross chick is old, its metabolism is . \(m(10)=4\) means that when an albatross chick is old, its metabolism is .    

Suppose \(f(x)=\dfrac{10\ln(x)}{\sqrt{x}}.\) To numerically estimate the value of \(f\,’\,(2)\), accurate to one decimal place, fill out the tables below. Be sure to round to the exact number of decimal places required!  Desmos (click to reveal)   \(b\to 2^-\) average rate of change 1.9   \(b\to 2^+\) average rate of change 2.1 From our tables we conclude that \(f\,’\,(2)=\) .

Use the graph of \(f(x)\) to fill in the blanks. If a value does not exist, type DNE.   \(\displaystyle\lim_{x\to 4^-}f(x)=\) \(\displaystyle\lim_{x\to 4^+}f(x)=\) \(\displaystyle\lim_{x\to 4}f(x)=\) \(f(4)=\) Is \(f(x)\) continuous at \(x=4\)?

Exam 2 – Makeup Challenge Problem.pdf Gradescope Submission Link

The maximum theoretical thermodynamic efficiency of a heat engine operating between hot and cold reservoirs is a function of which of the following?

In the figure, R1 = R2 and cm represents the center of mass of the object.  The rotational inertia about an axis through point P1 is I1, the rotational inertia about an axis through point P2 is I2, and the rotational inertia about an axis through the cm is Icm.  The relationship among the moments is

Use the information below to answer the four (4) following questions:A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below. A point or points at which the object has positive velocity and zero acceleration is(are)