From the list below, supply the words needed to complete the paragraph. Some words will not be used. evoke, inane, expatriate, sere, heinous, enhance, frowzy, postulate. Jerry squinted and ran his hand through his _____ mop of hair. The Pacific sun was already high in the sky, and he had a lot of work to accomplish before his guests arrived that evening. Originally from a Minnesota dairy, Jerry had lived on the tiny Micronesian island for over sixteen years. He never really considered himself to be a[n] _____, but then again, he didn't plan to return to the United States, either. Thinking that it might be a good idea to _____ his front yard before his visitors arrived, Jerry grabbed a machete and walked to the coconut grove in front of his shack. Huffing, Jerry chopped at the _____, withered fronds hanging against the trunks of the palm trees. When he finished cutting the fronds, he gathered the stray coconuts-some months old-and piled them in the corner of his yard. The yard looked sharp, even with Jerry's dilapidated shack in the background. As a bonus, Jerry decided to place two rows of tiki-torches along the path to the shack. Jerry thought that such trinkets were _____, but he wanted his two nieces from Cleveland to get the total island experience.

From the list below, supply the words needed to complete the paragraph. Some words will not be used. postulate, heinous, evoke, impeccable, expatriate, unctuous. Jordan sat at the helm and surveyed the broken radio before speaking to Candace. "This is not going to be easy. You're going to have to _____ all the strength you have in order to succeed." In her typical sarcastic manner, Candace responded to Jordan in a[n] _____ tone. "Oh, really? Thank goodness you told me; I had _____ that swimming two miles through an oil slick would be easy!" Candace walked over to the porthole and looked at the horizon. The line where the earth met the sky was tilted by at least seven or eight degrees; the Nittany was definitely taking on water. The wounded tanker in the distance wasn't doing much better; from the Nittany's bridge, Jordan could tell where the tanker's hull had ruptured by a black swirl slowly meandering through the crystal clear water. "Do you remember what you're doing?" "Piece of cake," said Jordan. "Be sure to give him the proper coordinates; I'm not going down with the ship." "Oh, don't worry," snapped Candace. "Any shark that eats you will immediately spit you back out." "Ha-ha. Thanks for the _____ image of my certain death." "Oh, relax. Once we get out of this, I'll treat you to a[n] _____ lobster dinner on Maui. See ya later!" With that, Candace walked out of the bridge and jumped over the handrail. Jordan didn't even hear the splash.

From the list below, supply the words needed to complete the paragraph. Some words will not be used. rancor, ostensible, extol, clement, adamant, disparity, cliche. I wish that I could _____ your recent work, but as the _____ goes, workers like you are a dime a dozen. I've been keeping you on the payroll despite your recent incompetence, but it must end now. The president is _____ about cutting unnecessary costs, so I'm afraid that I'm going to have to let you go. I can't be _____ with you any longer.

Complete the following sentences by choosing the word that best fits the context, based on information you infer from the use of the italicized word. Some word pairs will be antonyms, some will be synonyms, and some will simply be words often used in the same context. The barrister was good at her job, but still had compunctions when the courts ____ clients whom she suspected were, in fact, guilty. A. acquitted, B. befuddled, C. basked, D. connived, E. chastised.

Find the distance between the points in each pair. Round to the nearest tenth. (-2, 9) and (6, 0)

From the list below, supply the words needed to complete the paragraph. Some words will not be used. charlatan levity naive bask enraptured fickle hoax mundane amicable A. When the ___ citizens of Reynoldsville finally realized that their forty-cent bottles of miracle sap contained nothing more than licorice extract and whiskey, they formed a lynch mob and searched for the ___ who had sold the fake elixir. Fortunately, Colonel Britton, the quack they were looking for, had already taken his wagon and quietly left town before down. He rode nonstop for a full day until, in his usual routine, he pulled far off the trail and spent a day restocking his miracle sap, occasionally breaking to partake of some himself. ___ by the beautiful scenery of the Black Hills, Britton didn't waste his opportunity to ___ in the low autumn sun for the reminder of the afternoon. While most of his clientele were desensitized to the beauty of nature after spending harsh lives in it, Britton never once considered his private outings to be ___; if he didn't spend at least a few hours enjoying nature every week, he had trouble maintaining his ___ demeanor whenever he rolled into a new town. If Britton didn't at least appear to be happy, people were not going to purchase his tonic, whether it was a[n] ___ or not. His customers were very ___ about spending their money; if they had even the slightest notion that Britton's product was a scam, they would not buy it.

From the list below, supply the words needed to complete the paragraph. Some words will not be used. condone, officious, nuance, cult, connoisseur, credence, torpor, dilettante. The chef, tucked away in the kitchen, nervously awaited the report from the latest critic. Knowing that Mr. Tahoma was a[n] _____ of Peruvian cuisine and a weekly newspaper columnist with a[n] ____ following, the chef hoped that the waiters refrained from the _____ behavior that well-known food critics must often endure from servers. The chef had run the restaurant for twenty-eight years; he was certainly not a[n] _____ in matters of cooking, but owing to a decline in customers, he worried about the fate of the business. He could only hope that Mr. Tahoma would rave about the many subtle _____ in the meal. A positive review, combined with the _____ accorded to the column, might be all that the chef needed to save the restaurant.

From the list below, supply the words needed to complete the paragraph. Some words will not be used. magnanimous expatriate impeccable emulate impound collaborate contrite A. "Don't _____ me, kid-unless you want to spend time in the slammer, too," Buddy laughed as he put his hands in the air and glanced around. "But if you're really interested, maybe we can _____ on 'helping' you pick the winning horse. " Lucas didn't return his uncle's smirk, and buddy became ____ _ Lucas never really adapted to conversing through a sheet of Plexiglas, and the tinny sound of Buddy's musing through the two-way intercom made him uncomfortable. Lucas came to the prison only because the police were going to _____ Buddy's car if no one removed it from the credit union parking lot, and Lucas thought that he was being _____ by mentioning that he, like Buddy, had an interest in horse racing. From the list below, supply the words needed to complete the paragraph. Some words will not be used. evoke inane expatriate sere heinous enhance frowzy enunciate B. Jerry squinted and ran his hand through his _____ mop of hair. The Pacific sun was already high in the sky, and he had a lot of work to accomplish before his guests arrived that evening. Originally from a Minnesota dairy, Jerry had lived on the tiny Micronesian island for over sixteen years. He never really considered himself to be a[n] ____ _ but then again, he didn't plan to return to the United States, either. Thinking that it might be a good idea to _____ his front yard before his visitors arrived, Jerry grabbed a machete and walked to the coconut grove in front of his shack. Huffing, Jerry chopped at the ____ _ withered fronds hanging against the trunks of the palm trees. When he finished cutting the fronds, he gathered the stray coconuts-some months

From the list below, supply the words needed to complete the paragraph. Some words will not be used. dossier, august, semblance, indefatigable, picayune, philatelist, albeit, behest. Like many residents of Crystal Point, Janine walked to the beach every evening to witness the _____ beauty of the sun setting over the Pacific. The white dunes were the best place to experience the beautiful event, _____ several barges on the horizon diminished the view. They were a[n] _____ detail to Janine; it would require more than a few dots on the horizon to distract her from the blazing sky. Today, as Janine approached the water, she was amused to find a large mound of sand in the vague _____ of a whale. The Williards must have visited the beach; they have three _____ children who readily spend entire days creating sand sculptures.

From the list below, supply the words needed to complete the paragraph. Some words will not be used. droll gamut effigy austere duplicity abhor extrovert A. Monique was a[n] ____ who loved dealing with people, but she never thought that she would satisfy her need for socializing by selling used cars. She always ____ salespeople, but after becoming one, Monique realized that only a fraction of the ____ of salespeople indulge in the ____ and false promises that make dissatisfied customer angry enough to burn _____ of them.

From the list below, supply the words needed to complete the paragraph. Some words will not be used. fluctuate, exult, cajole, inscrutable, expound, metier, acrimony, harry. Councilwoman Moore stepped up to the podium. "I don't think I need to _____ upon reasons for voting against the proposed construction; I thought that the message was clear enough at the last meeting-when you all opposed it as well. Obviously, someone has _____ a few of you into changing your opinion since last month, and your sudden, _____ decision to yield to Beta-Rad Enterprises bothers me a great deal. What happened to the surplus of _____ toward Beta-Rad from the last meeting? Don't you remember how we _____ in our victory over the radioactive waste dump? For two years, we've listened to Beta-Rad executives _____ us, and we finally had the chance to stop it for good. How could the opinions of fifteen people possibly _____ this much?"

From the list below, supply the words needed to complete the paragraph. Some words will not be used. abate decorum dole abhor droll austere duplicity B. Typhoon Paka hammered the island of Guam for twelve hours before the winds ____. Gusts over two hundred miles an hour devastated the previously green island, creating ____ living conditions for residents in the weeks to come, especially for the estimate five thousand people who lost their homes. Residents able to witness Paka in action were astounded by the serious but almost ____ sight of Paka's invisible forces tossing around automobiles, dumpsters, and palm trees as though they were children's toys. In the days following Paka, residents adhered to traditional post-typhoon ____ by cleaning up hundreds of tons of debris, checking on the condition of friends and neighbors, repairing property, and, because of the lack of electricity, hosting mass barbecues before food perished in warm refrigerators. Luckily, food was not in short supply, but water had to be ____ out by several agencies in the weeks following the tempest.

From the list bellow, supply the words needed to complete the paragraph. some words will not be used. incognito feasible dour fiasco metier lethargy balk omniscient harry B. "Hey, Jye; I think you've found your ____." "Colud be." Jye glanced up only long enough to catch a glimpse of Neve. Typing rapidly, Jye intermittently glanced at the stack of printed matrixes next to the keyboard. Usually a[n] ___ person who remained hidden in his software-engineer cubicle all day, Jye adopted a manner bordering on cynicism and ____ getting him to do tech support beyond his cubicle walls was often a[n] ___ that created more trouble that it solved. Neve was caught completely off-guard when Jye didn't ____ at the company's request that he test the system's network security by hacking into the company database. Though Jye had his ways, everyone knew that he was the ____ office authority when it came to network security protocol. It simply wouldn't have been ____ to use anyone else to test the integrity of Pentacode's newest software. Additionally, Jye's newfound energy changed his manner so much that he might as well have been ___ to those who didn't see him every day; when his attitude changed, his wardrobe and hairstyle changed as well.

(a) Prove the following partial converse to the uniform limit theorem: Let $f_{n}: X \rightarrow \mathbb{R}$ be a sequence of continuous functions, with $f_{n}(x) \rightarrow f(x)$ for each $x \in X$. If f is continuous, and if the sequence $f_{n}$ is monotone increasing, and if X is compact, then the convergence is uniform. [We say that $f_{n}$ is monotone increasing if $f_{n}(x) \leq f_{n+1}(x)$ for all n and x.] (b) Give examples to show that this theorem fails if you delete the requirement that X be compact, or if you delete the requirement that the sequence be monotone.