Use logarithmic differentiation to evaluate f'(x). $f ( x ) = x ^ { 2 } \cos x$

Determine whether the sequence is an arithmetic sequence. If it is, state the common difference. 7, 6, 5, 4, ...

Estimate the sum or difference.

$$2 \frac { 3 } { 5 } - 1 \frac { 3 } { 8 }$$

Estimate: __________

In the search to reduce thermal pollution and take advantage of renewable energy sources, some people have proposed that we take advantage of such sources as discharges from electric power plants. geothermal energy, and ocean thermal energy. Although many of these sources contain an enormous amount of energy, the amount of work they are capable of producing is limited. How might you use the work potential to assign an "energy quality" to these proposed sources? Test your proposed "energy quality" measure by applying it to the ocean thermal source. Where the temperature 30 m below the surface is perhaps $5^{\circ} \mathrm{C}$ lower than at the surface. Apply it also to the geothermal water source, where the temperature 2 to 3 km below the surface is perhaps $150^{\circ} \mathrm{C}$ hotter than at the surface.

Determine whether the statement is true or false, and justify your answer. If the column sums of the consumption matrix are all less than 1, then the Leontief matrix is invertible.

Find the areas of the parallelograms whose vertices are given. A(1, 0, -1), B(1, 7, 2), C(2, 4, -1), D(0, 3, 2)

$$180 ^ { \circ } < \alpha < 360 ^ { \circ }$$

and

$$\cos \alpha = \frac { 8 } { 17 }$$

. Find the following.

$$\sin \frac { \alpha } { 2 }$$

Work cooperatively. Solve each equation or inequality. $\frac{4}{x}=\frac{6}{x^{2}}$

Write each equation in standard form. $x+\frac{1}{3} y=\frac{2}{9}$

find a set of parametric equations of the line. (There are many correct answers.) Passes through (-4, 5, 2) and is parallel to the xy-plane and the yz-plane

A migrating salmon heads in the direction N

$$45 ^ { \circ }$$

E. swimming at 5 mi/h relative to the water. The prevailing ocean currents flow due east at 3 mi/h. Find the true velocity of the fish as a vector.

Design a circuit to amplify the difference between two inputs by 2.5. (a) Use only one op amp. (b) Use two op amps.

(a) identify the claim and state

$$H _ { 0 }$$

and

$$H _ { a }$$

, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology. A real estate agent claims that there is no difference between the mean household incomes of two neighborhoods. The mean income of 12 randomly selected households from the first neighborhood is $32,750 with a standard deviation of$1900. In the second neighborhood, 10 randomly selected households have a mean income of $31,200 with a standard deviation of$1825. At

$$\alpha = 0.01$$

, can you reject the real estate agent’s claim? Assume the population variances are equal.

If $n(A)=30, n(B)=40$ and $n(A \cup B)=45$ find $n(A \cap B)$