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3.3 If $f(x) = x^2$, prove from first principles that $\lim_{x \to 2} f(x) = 4$. (Hint: it is sufficient to prove Eq. 3.1 assuming that $\delta = |x - 2| < 1$, and you may use the general relation $|a + b| \le |a| + |b|$ for any $a$, $b$.)

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Exercise 3: Part A The adjacent figure is a parallelogram, calculate \( x \) and \( y \). Part B \( A B C D \) is a parallelogram such that: \( A D=3 \mathrm{~cm} \) and \( A B=2 A D \). Calculate the perimeter of \( A B C D \).

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How is acupuncture, after dealing with chronic migraines for several years, helpful?

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Which of the following vitamins is necessary for production of collagen? Multiple Choice Vitamin C Thiamine Vitamin D Biotin

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A tax law change that encourages saving (all else equal) would Group of answer choices have no effect on interest rates. increase interest rates. decrease interest rates. increase the demand for loanable funds. decrease the supply of loanable funds. No

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Calculate $\frac{dy}{dx}$. You need not expand your answer. $y = (x + 9)(x^2 - 9)$

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EXIBIT 3.1 Samson Edward Salisbury, a citizen of Australia and an executive with Queensland Consolidated Oil PLC quit his \$800,000 per year job in 2016 to start his own business, Melbourne Chemical Company (MCC). He now owns and operates five firms that produce several types of chemicals for sale to businesses and households, mostly in Australia, New Zealand, Papua New Guinea, Singapore, India, and China. Although MCC has subsidiaries in New Zealand, India, and Singapore, its global headquarters are located in the Australian city of Sydney. MCC's headquarters are housed in four commercial building, which he inherited from his great-grand mother and one of Australia's most important chemical engineers, Dame Margaret Ann Salisbury. Part of Salibury's inheritance, \$5,000,000, was used to purchase equipment (mostly large and extremely expensive computing systems) for his five businesses. Before he inherited the buildings in which MCC's headquarters are located, they had been rented to Gold Coast Mining Consultants, PLC, for \$65,000 per month. Last year (2020) MCC had total revenues of \$110,000,000; supplies cost \$16,000,000; employees received \$45,000,000; and total advertising expenditures were \$25,000,000. Total depreciation expenditures for 2020 were \$4, 500,000. Assume a market interest rate of 5 percent. 15. What were MCC's accounting profit (ra) in 2020? 1. \$86,000,000 2. \$17,670,000 3. \$92,330,000 4. \$6,330,000 5. \$19,500,000

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Consider an bar made of 6061-T6 aluminum having length of 10 inches at a temperature of 25 degrees Celsius. If the bar is placed in a cooler at a temperature of -3 degrees Celsius. Calculate the final length (in inches) of the bar after sufficient time has passed since being placed in the cooler. NOTE: Material properties were taken from textbook (located on back cover). 10

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Application 4 From Taxonomy to Phylogeny Phylum Subphylum Class Order Family Arthropoda Hexapoda Insecta Hemiptera Cicadellidae Arthropoda Hexapoda Entognatha Symphypleona Sminthuridae Arthropoda Chelicerata Arachnida Araneae Araneidae Arthropoda Hexapoda Entognatha Entomobryomorpha Isotomidae Arthropoda Hexapoda Insecta Coleoptera Buprestidae 14. Given the information you have on the taxonomy of these species, draw as accurate a tree as possible on the next slide. Hint: you may need to move the images around! Remember that while Linnaeus classified species based on similarity, these levels now reflect our understanding of phylogenetic relationships!

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Section 1.7 1. For $F = 500$ lb, $V = 100$ mph, and $l = 3$ ft, show that the Reynolds number and force coefficient (Eqs. 1.18 and 1.19) have the same values in FPS and SI units. Calculate for both air and water under standard conditions. Tables 1 and 2 give conversion fac- tors and numerical values.

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