Water temperature affects the growth rate of brook trout. The table shows the amount of weight gained by brook trout after 24 days in various water temperatures.

Temperature (degrees C)	15.5	17.7	20.0	22.4	24.4
Weight gained (g)	37.2	31.0	19.8	9.7	29.8

If \(W(x)\) is the weight gain at temperature \(x\), construct a table of estimated values for \(W'\) and sketch its graph. What are the units for \(W'(x)\)?

\(\operatorname*{lim}\limits_{x \rightarrow \infty} \dfrac{10^8 x^5 + 10^6 x^4 + 10^4 x^2}{10^9 x^6 + 10^7 x^5 + 10^6 x^4} =\)

Find an equation of the plane through the point \(\left(-1, \dfrac{1}{2}, 3\right)\) and with normal vector \(\mathbf{i} + 4 \mathbf{j} + \mathbf{k}\).

Evaluate the integral: \(\int x^2 \ln x d x\)

The curves with equations \(x = a \sin n t\), \(y = b \cos t\) are called Lissajous figures. Investigate how these curves vary when \(a\), \(b\), and \(n\) vary. (Take \(n\) to be a positive integer.)