a. Which

$$K _ { \mathrm { eq } }$$

corresponds to a negative value of

$$\Delta G ^ { \circ } , K _ { \mathrm { eq } } = 1 0 0 0 \text { or } K _ { \mathrm { eq } } = . 0 0 1 ?$$

b. Which

$$K _ { \mathrm { eq } }$$

corresponds to a lower value of

$$\Delta G ^ { \circ } , K _ { \mathrm { eq } } = 1 0 ^ { - 2 } \text { or } K _ { \mathrm { eq } } = 1 0 ^ { - 5 } ?$$

In Fig. 5–25, how much is $R_\text{EQ}$ if $R_1=2.2\text{ k}\Omega$ and $R_2=220\space\Omega$?

Find the area of the surface.
The part of the cylinder $y^2+z^2=9$ that lies above the rectangle with vertices $(0,0),(4,0),(0,2)$, and $(4,2)$

At a certain temperature, $K_{\text {eq }}$ is $2.2 \times 10^{-3}$ for the reaction $2 \mathrm{~ICl}(g) \rightleftharpoons \mathrm{I}_2(g)+\mathrm{Cl}_2(g)$ Now calculate the $K_{\text {eq }}$ value for the reaction

$$\mathrm{I}_2(g)+\mathrm{Cl}_2(g) \rightleftharpoons 2 \mathrm{~ICl}(g)$$

In Fig. 5–28, solve for $G_1$, $G_2$, $G_3$, $G_4$, $G_\text{T}$, and $R_\text{EQ}$.

Find the limit.

$$\lim _{h \rightarrow 0} \frac{(1+h)^{-2}-1}{h}$$

Graph the function represented by each side of the equation in the same viewing rectangle and solve for x.

$$2 x+6=4 x-2 x+8-2$$

Find the absolute extrema of $f(x, y)=2 \cos x+ 3 \sin y$ on the rectangle $\{(x, y) | 0 \leq x \leq 4,0 \leq y \leq 3\}$

Use Eq. earlier to show that $R_{i 2} \simeq 4 \mathrm{M} \Omega$.

a) Derive Equation b) Derive Eq.

Show mathematically how Equation $K_{\mathrm{eq}}=\frac{\left[\mathrm{A}^{-}\right][\mathrm{HB}]}{[\mathrm{HA}]\left[\mathrm{B}^{-}\right]}$ can be converted to Equation $K_{\mathrm{eq}}=\frac{K_{\mathrm{a}(\mathrm{HA})}}{K_{\mathrm{a}(\mathrm{HB})}}$ and $\log _{10} K_{\mathrm{eq}}=\log _{10} K_{\mathrm{a}(\mathrm{HA})}-\log _{10} K_{\mathrm{a}(\mathrm{HB})}$.

What is the area of the rectangle? $12 in \times 8 in$. A. 20 sq. in. B. 40 sq. in. C. 96 sq. in. D. 106 sq. in.

Graph

$$y = e ^ { x } \text { and } y = 1 + x + \frac { x ^ { 2 } } { 2 } + \frac { x ^ { 3 } } { 6 } + \frac { x ^ { 4 } } { 24 }$$

in the same viewing rectangle.

In Fig. 23–22, solve for $I_1$, $I_2$, $I_\text{T}$, and $X_{\text{C}_{\text{EQ}}}$.