China was divided into spheres of influence; __ .

Compare the values of $\Delta$y and dy if x changes from 1 to 1.05. What if x changes from 1 to 1.01? Does the approximation $\Delta y \approx d y$ become better as $\Delta$x gets smaller? f(x) = e$^{2 x-2}$

In this exercise, make the given changes in the indicated examples of this section, and then answer the given questions.

In the first line of Example $1$, change the $5$ to $-3$ and the $-19$ to $14$. What other changes must then be made in the first paragraph?

Why were spheres of influence established in China?

Flurry, Inc., is expanding into China. The company must decide where to locate and how to finance the expansion. Identify the financial statement where these decision-makers can find the given information about Flurry, Inc. In some cases, more than one statement will report the needed data.

k. Selling, general, and administrative expenses

What geographical challenges were faced by China's early rulers in their efforts to unify China or make alliances with peoples outside of China?

Give a ballpark estimate of the number of seats in a typical major league ballpark.

Underline each predicate adjective in the following sentences.

Example 1. Did the baby seem $\underline{\text{restless}}$ and $\underline{\text{nervous}}$ this morning?

Does the soup taste too salty to you?

Adolph Ball Company is constructing a golf course in Scorpion Gulch. The plot for one of the putting greens is shown in figure. To estimate the area of the green, Mr. Ball draws parallel lines 10 (scale) ft apart and measures their lengths (feet). From the information given in the table, figure out about how many square feet of grass sod Mr. Ball must purchase to cover the green. Describe how you find the answer. Why can't the fundamental theorem of calculus be used to find this area?

Applying Concepts Think about what acid and what base would react to form each of the following salts. When each of the salts is dissolved in water, will its solution be acidic, basic, or neutral? If not neutral, use an equation to explain why. a) $\mathrm{NH}_4 \mathrm{Cl}$ c) $\mathrm{LiC}_2 \mathrm{H}_3 \mathrm{O}_2$ b) $\mathrm{NaCl}$ d) $\mathrm{NH}_4 \mathrm{C}_2 \mathrm{H}_3 \mathrm{O}_2$

Comet Halley The orbit of Comet Halley is an ellipse whose major axis is $3.34 \times 10^9$ miles long, and whose minor axis is $8.5 \times 10^8$ miles long. What is the eccentricity of the comet's orbit?

Simplify. Rationalize all denominators. Assume that all the variables are positive. $4 \sqrt{216 y^{2}}+3 \sqrt{54 y^{2}}$

Por un salto en el tiempo (time warp) un

hombre prehistórico llega a tu casa y hace las siguientes cosas.

Explícate cómo se hacen las cosas en el mundo moderno.

MODELO Se bana en la cocina.

¡No te bañes en la cocina! ¡Báñate en el baño!

Se lava los dientes con una toalla.

The function $f(x)$ changes value when $x$ changes from $x_0$ to $x_0+d x$. Find the change $\Delta f=f\left(x_0+d x\right)-f\left(x_0\right)$.

$$f(x)=x^{-1}, \quad x_0=0.5, \quad d x=0.1$$