Decide which form of the vocabulary word in parentheses best completes the sentence. The form given may be correct. Write your answer on the answer line.

The $\underline{?}$ of Rebecca's ideas into the rebuttal strengthened the debate team's position. (incorporate) _____________________

Compare and contrast the asteroid belt and the Kuiper belt.

Update your journal with the things you have learned since the last entry. You should include such things as those listed here.

• The one most important thing you have learned in studying last Chapter .

• Which boxes you have been working on in the "define, understand, do, apply" table.

• How to write from memory some special, well-known series.

• How you find a power series for a given function, either by equating derivatives or by operating on another known series.

• What it means for a sequence or series to converge.

• How you determine the accuracy of a function value found by series.

• Any ideas about series that are still unclear.

A tile setter cuts a piece of tile to a desired length. He then uses this tile as a pattern to cut a second tile congruent to the first. He uses the first two tiles to cut a third tile whose length is the sum of the measures of the first two tiles. Prove that the measure of the third tile is twice the measure of the first tile. Prove each theorem.

In Exercise given below, find the Taylor series at x=0 of the given function. Use suitable operations (differentiation, substitution, etc.) on the Taylor series at x=0 of $\frac{1}{1-x}, e^x$, or $\cos x$. These series are derived in Examples mentioned and Check Your Understanding pf the said Problem.

$$1-e^{-x}$$

In Exercise given below, find the Taylor series at x=0 of the given function. Use suitable operations (differentiation, substitution, etc.) on the Taylor series at x=0 of $\frac{1}{1-x}, e^x$, or $\cos x$. These series are derived in Examples mentioned and Check Your Understanding pf the said Problem.

$$x \sin x^2$$

Suppose that array temp is as defined. Write C++ statements to accomplish the following:

a. Output the contents of the first row and first column element of temp.
b. Output the contents of the first row and last column element of temp.
c. Output the contents of the last row and first column element of temp.
d. Output the contents of the last row and last column element of temp.

For the following telescoping series, find a formula for the nth term of the sequence of partial sums $\left\{S_{n}\right\}$. Then evaluate $\lim _{n \rightarrow \infty} S_{n}$ to obtain the value of the series or state that the series diverges. $\sum_{n=-3}^{\infty} \frac{10}{4 k^{2}+32 k+63}$

In what way did Boas's understanding of race and culture challenge prevailing ideas that had defined Anglo-Saxon superiority and "Negro" inferiority? What fundamental assumption about race did his anthropological work overturn?

The taxi ride cost $\$1.40$ plus $35\cancel{\mathrm{c}}$ for each tenth of a mile. What was the average cost per mile for a $4$-mile taxi ride?

Use properties of power series, substitution, and factoring of constants to find the first four nonzero terms of the Maclaurin series for the following functions. Use the Maclaurin series $( 1 + x ) ^ { - 2 } = 1 - 2 x + 3 x ^ { 2 } - 4 x ^ { 3 } + \cdots$ for -1<x<1. $\frac { 1 } { ( 3 + 4 x ) ^ { 2 } }$

Four radioactive decay series are known-three naturally occurring, and one beginning with the synthetic isotope ${ }_{94}^{241} \mathrm{Pu}$. To which of these decay series does the isotope ${ }_{86}^{219} \mathrm{Rn}$ belong? To which series does ${ }_{86}^{220} \mathrm{Rn}$ belong? Each isotope in these series decays by either alpha emission or beta emission. How do these decay processes affect the mass number?

Write out each sentence below to tell about problems in school. Follow the model. Modelo: Carlos / entender / nada - Carlos no entiende nada. tú / traer los materiales a clase / nunca

Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend.

$$\frac{9 y+18-11 y^2+12 y^3}{4 y+3}$$