Each of the following aldehydes or ketones is known by a common name. Its substitutive IUPAC name is provided in parentheses. Write a structural formula for each one. (a) Chloral (2,2,2-trichloroethanal) (b) Pivaldehyde (2,2-dimethylpropanal) (c) Acrolein (2-propenal) (d) Crotonaldehyde [(E)-2-butenal] (e) Citral [(E)-3,7-dimethyl-2,6-octadienal] (f) Diacetone alcohol ( 4-hydroxy-4- methyl-2-pentanone) (g) Carvone ( 5-isopropenyl-2-methyl-2-cyclohexenone) (h) Biacetyl (2,3-butanedione)

Convert each of the following functional class IUPAC names to a substitutive name. (a) Dibenzyl ketone (b) Ethyl isopropyl ketone (c) Methyl 2,2-dimethylpropyl ketone (d) Allyl methyl ketone

The common names and structural formulas of a few aldehydes follow. Provide an IUPAC name for each. (a) Isobutyraldehyde (b) Glutaraldehyde (c) Glyceraldehyde (d) Vanillin

(a) Write structural formulas and provide IUPAC names for all the isomeric aldehydes and ketones that have the molecular formula $\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}$. Include stereoisomers. (b) Which of the isomers in part (a) yield chiral alcohols on reaction with sodium borohydride? (c) Which of the isomers in part (a) yield chiral alcohols on reaction with methylmagnesium iodide?

Find the following. $\int\left(6 t^{2}-8 t+7\right) d t$

Determine concavity and the x-values where points of inflection occur. Do not sketch the graphs. $y=\frac{1}{10} x^{5}-3 x^{3}+17 x+43$

Write the structure of the principal organic product formed in the reaction of 1-propanol with each of the following reagents: (a) Sulfuric acid (catalytic amount), heat at $140^{\circ} \mathrm{C}$ (b) Sulfuric acid (catalytic amount), heat at $200^{\circ} \mathrm{C}$ (c) Dimethyl sulfoxide (DMSO), oxalyl chloride $\left[(\mathrm{COCl})_{2}\right]$, triethylamine $\left[\mathrm{N}\left(\mathrm{CH}_{2} \mathrm{CH}_{3}\right)_{3}\right]$ (d) Pyridinium chlorochromate (PCC) in dichloromethane (e) Potassium dichromate $\left(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\right)$ in aqueous sulfuric acid, heat (f) Sodium amide $\left(\mathrm{NaNH}_{2}\right)$ (g) Acetic acid in the presence of dissolved hydrogen chloride

Show that the function $f(x)=\frac{x}{x+1}$ is increasing on any interval not containing x=-1.

Solve the systems algebraically.

$$\left\{\begin{array}{l} {\frac{1}{2} z-\frac{1}{4} w=\frac{1}{6}} \\ {\frac{1}{2} z+\frac{1}{4} w=\frac{1}{6}} \end{array}\right.$$

Based on the E1 mechanism for the conversion of a tertiary alkyl chloride to an alkene as summarized in arrows 3 and 4, which arrow(s) correspond(s) to exothermic processes? A. Arrow 3 B. Arrow 4 C. Both 3 and 4 D. Neither 3 nor 4

In a discussion of an inferior good, Persky$^{4}$ solves an equation of the form $u_{0}=A \ln \left(x_{1}\right)+\frac{x_{2}^{2}}{2}$ for $x_{1},$ where $x_{1}$ and $x_{2}$ are quantities of two products, $u_{0}$ is a measure of utility, and A is a positive constant. Determine $x_{1}.$

Express the area under the curve $y=x^{4}+5 x^{2}+x$ from 2 to 7 as a limit.

Find the volume of the cone. Round your answer to the nearest tenth. Radius = 2 ft, Height = 6 ft

A small-appliance manufacturer finds that it costs $9000 to produce 1000 toaster ovens a week and$12,000 to produce 1500 toaster ovens a week. Express the cost as a function of the number of toaster