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Two techniques for fitting models to data are called direct $\underline{\hspace{1.5cm}}$ and least squares $\underline{\hspace{1.5cm}}$.

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A relation that assigns to each element $x$ from a set of inputs, or $\underline{\hspace{1.5cm}}$ , exactly one element $y$ in a set of outputs, or $\underline{\hspace{1.5cm}}$, is called a $\underline{\hspace{1.5cm}}$.

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The graph of a function $f$ is the collection of $\underline{\hspace{1.5cm}}$ $(x, f(x))$ such that $x$ is in the domain of $f$.

Determine whether the equation represents $y$ as a function of $x$.

$$16 x-y^4=0$$

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The graph of a function $f$ is the collection of $\underline{\hspace{1.5cm}}$ $(x, f(x))$ such that $x$ is in the domain of $f$.

Use the Direct Comparison Test to determine the convergence or divergence of the series.

$$\sum_{n=1}^{\infty} \frac{1}{3 \sqrt[4]{n}-1}$$

Gotcha Co. makes one model of radar gun used by law enforcement officers. All direct materials are added at the beginning of the manufacturing process. Information for the month of September follows:

Do you agree or disagree with this statement: "Representative democracy works better than direct democracy in large countries." Defend your answer.

What metaphors, or direct comparisons, does the speaker in Petrarch's Sonnet $61$ use to describe his state of mind? Find two examples.

Copy the sentence in your notebook. Underline the words of direct address and add punctuation where necessary.

Choir members please stand straight.

Let $I$ be an arbitrary nonempty index set and for each $i \in I$ let $N_{i}$ be a left $R$ -module. Let $M$ be a right $R$ -module. Prove the group isomorphism: $M \otimes\left(\oplus_{i \in I} N_{i}\right) \cong \oplus_{i \in I}\left(M \otimes N_{i}\right)$ where the direct sum of an arbitrary collection of modules is defined in Exercise 20 , Section $3 .$ IUse the same argument as for the direct sum of two modules, taking care to note where the direct sum hypothesis is needed - cf. the next exercise. $.$ .

If G is the internal direct product of $H_{1}, H_{2}, \ldots, H_{n}$, prove that G is isomorphic to $\prod_{i} H_{i}$.

In this exercise, use the Direct Comparison Test to determine the convergence or divergence of the series.

$$\displaystyle\sum_{n=2}^{\infty} \frac{1}{\sqrt{n}-1}$$

In this exercise, use the Direct Comparison Test to determine the convergence or divergence of the series.

$$\displaystyle\sum_{n=0}^{\infty} \frac{3^n}{4^n+5}$$