Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist.

$$f\left(x_1, x_2\right)=x_1^2+x_2^2, \quad x_1+x_2=1$$

Find the sum of each arithmetic series. The first 100 terms of the series

$$100 + 98 + 96 + 94 + \cdots$$

Write as an algebraic expression.

Suppose $w$ was Lisa's weight last year. Lisa lost $7$ pounds this year. Write an expression for Lisa's weight this year.

Use the concept of marginal utility to explain the following: Newspaper vending machines are designed so that once you have paid for one paper, you could take more than one paper at a time. But soda vending machines, once you have paid for one soda, dispense only one soda at a time.

When you exhale, all of the air in your lungs must exit through the trachea. If you exhale through your nose, this air subsequently leaves through your nostrils. The area of your nostrils is less than that of your trachea. How does the speed of the air in the trachea compare to that in the nostrils?

Determine whether each of the statements is true or false, and explain why. In a fair game, the elements of the payoff matrix must sum to 0.

Why do experiments usually test only one variable at a time?

Find the sum.

$$\sum _ { k = 2 } ^ { 5 } ( 5 k )$$

Find the Taylor series at x = 0 for each function by modifying one of the Taylor series from this section.

sin x + cos x

Choose an appropriate data display for the situation. Explain your reasoning. percent of class participating in school clubs

Circle the word or words modified by the adverb in italics. On the blank, write $v$ if the adverb modifies a verb. Write $adj$. if the adverb modifies an adjective. Write $adv$. if the adverb modifies another adverb.\ ______I don’t think she was entirely sure what she had said.

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. $f(x)=\frac{x-4}{5-x}$

Identify the property that justifies each statement. $x=y, \text { so } y=x$

A particle P is in uniform circular motion, centered on the origin of an $x y$ coordinate system. At what values of $\theta$ is the vertical component $r_y$ of the position vector greatest in magnitude?