Let

$$f ( x ) = \frac { \cos x } { 1 + x ^ { 2 } }$$

. (a) Use a graphing device to graph f in an appropriate viewing rectangle. (b) Determine from the graph if f is even, odd, or neither. (c) Find the minimum and maximum values of f.

Find the length of the curve $y=\ln (\csc x)$ from $x=\pi / 6$ to $x=\pi / 4$

How can the verb tener be used in a phrase to answer this question? ¿Marcela quiere más agua? Creo que ella ____________________________.

In each case, write x as a linear combination of the orthogonal basis of the subspace U. (a)

$$\begin{array} { l } { \mathbf { x } = ( 13 , - 20,15 ) } \\ { U = \operatorname { span } \{ ( 1 , - 2,3 ) , ( - 1,1,1 ) \} } \end{array}$$

, (b)

$$\begin{array} { l } { \mathbf { x } = ( 14,1 , - 8,5 ) } \\ { U = \operatorname { span } \{ ( 2 , - 1,0,3 ) , ( 2,1 , - 2 , - 1 ) \} } \end{array}$$

Elemental Li and Na are prepared by electrolysis of a molten salt, whereas K, Rb, and Cs are prepared by chemical reduction.

In general terms, explain why the alkali metals cannot be prepared by electrolysis of their aqueous salt solutions,

Miley and Damian determined formulas they could use to compute the first $n-$terms of the series Show that both representations for $S_{n}$ are equivalent.

Find the exact value of each quadrantal angle. If any are not defined, write undefined. $\sin \left( - 1530 ^ { \circ } \right)$

Find the period of the function and use the language of transformations to describe how the graph of the function is related to the graph of y= cos x. y = cos x/5

Besides anxiety, how might you realize that you are suffering from a somatoform or dissociative disorder?

A mass suspended from a spring oscillates in simple harmonic motion. The mass completes 2 cycles every second, and the distance between the highest point and the lowest point of the oscillation is 10 cm. Find an equation of the form

$$y = a \sin \omega t$$

that gives the distance of the mass from its rest position as a function of time.

Solve each equation and check your solution. $\frac{6}{5} x=-1$

Use any analytical method to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. You do not need to use the definition of the Taylor series coefficients.

Consider the function $f(x)=\frac{3 x-2}{x+3}$. Find $f^{\prime}(x)$ and draw its sign diagram.

Solve the following cryptarithms. Assume that no leading digit is a 0.

$$AT \\ EAST \\ \frac{+WEST}{SOUTH}$$