Evaluate each integral. $$\int_{1}^{5} y e^{4 x+y^{2}} d x$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).$$\int_{1}^{5} \int_{0}^{3}\left(x^{2} y+5 y\right) d x d y$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ). $$\int_{0}^{3} \int_{1}^{2}\left(x y^{3}-x\right) d y d x$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ). $$\int_{0}^{1} \int_{3}^{6} x \sqrt{x^{2}+3 y} d x d y$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).$$\int_{0}^{3} \int_{4}^{5} x \sqrt{x^{2}+3 y} d y d x$$

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Evaluate each integral.$$\int_{0}^{3} y e^{4 x+y^{2}} d y$$

$\frac{1}{2}\left(e^{4 x+9}-e^{4 x}\right)$

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Evaluate each double integral.$$\int_{0}^{1} \int_{2 x}^{4 x} e^{x+y} d y d x$$

Balance each redox reaction occurring in acidic aqueous solution.$$\begin{array}{l}{\text { a. } \mathrm{Zn}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Sn}(s)} \\ {\text { b. } \mathrm{Mg}(s)+\mathrm{Cr}^{3+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cr}(s)} \\ {\text { c. } \mathrm{MnO}_{4}-(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{Al}^{3+}(a q)}\end{array}$$

Copy and complete the two-column proof for the Congruent Supplement Theorem (Theorem 2.4). Then write a paragraph proof. (See Example 5.)$\begin{array}{ll}{\text { Given }} & {\angle 1 \text { and } \angle 2 \text { are supplementary. }} \\ {} & {\angle 3 \text { and } \angle 4 \text { are supplementary. }} \\ {} & {\angle 1 \cong \angle 4} \\ {\text { Prove }} & {\angle 2 \cong \angle 3}\end{array}$

The figure above shows the straight-line depreciationof a laptop computer over the first five years of itsuse. According to the figure, what is the average rateof change in dollars per year of the value of thecomputer over the five-year period?$$\begin{array}{l}{\text { (A) }-1,100} \\ {\text { (B) }-220} \\ {\text { (C) }-100} \\ {\text { (D) } \quad 100}\end{array}$$

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## Discussion

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## Recommended Questions

Evaluate each double integral.

$$\int_{0}^{1} \int_{2 x}^{4 x} e^{x+y} d y d x$$

Evaluate each integral.

$$\int_{1}^{5} y e^{4 x+y^{2}} d x$$

Balance each redox reaction occurring in acidic aqueous solution.

$$\begin{array}{l}{\text { a. } \mathrm{Zn}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Sn}(s)} \\ {\text { b. } \mathrm{Mg}(s)+\mathrm{Cr}^{3+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cr}(s)} \\ {\text { c. } \mathrm{MnO}_{4}-(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{Al}^{3+}(a q)}\end{array}$$

Copy and complete the two-column proof for the Congruent Supplement Theorem (Theorem 2.4). Then write a paragraph proof. (See Example 5.)

$\begin{array}{ll}{\text { Given }} & {\angle 1 \text { and } \angle 2 \text { are supplementary. }} \\ {} & {\angle 3 \text { and } \angle 4 \text { are supplementary. }} \\ {} & {\angle 1 \cong \angle 4} \\ {\text { Prove }} & {\angle 2 \cong \angle 3}\end{array}$

The figure above shows the straight-line depreciation

of a laptop computer over the first five years of its

use. According to the figure, what is the average rate

of change in dollars per year of the value of the

computer over the five-year period?

$$\begin{array}{l}{\text { (A) }-1,100} \\ {\text { (B) }-220} \\ {\text { (C) }-100} \\ {\text { (D) } \quad 100}\end{array}$$