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Find the area of the region bounded | Ch 5 - 5, 7th Edition

Single Variable Calculus | 7th Edition | ISBN: 9780538497831 | Authors: James W Nilsson ISBN: 9780538497831 151

Solution for problem 5 Chapter 5

Single Variable Calculus | 7th Edition

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Single Variable Calculus | 7th Edition | ISBN: 9780538497831 | Authors: James W Nilsson

Single Variable Calculus | 7th Edition

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Problem 5

Find the area of the region bounded by the given curves.

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Step 1 of 3

Diversity of Life II Notes Week 11 4/7/16 Dr. Donald Stewart – Fish Aquatic vertebrates with gills and limbs in the shape of fins Ex. ‘Blobfish’ – YES  There are exceptions Diversity ­25,000 living species (conservative estimate) to perhaps over 30,000 ­several hundred new species identified every year (many in Amazon and Philippines) ­482 families, 57 orders ­85 are jawless fishes ­850 are cartilaginous (sharks, stingrays and allies) ­everything else (over 23,000) are bony fishes, about 96% ­bones are comprised of Calcium Phosphate ­during hard times with little food available the fish can sequester phosphate out of their bones as emergency food source Most of the world (over two­thirds) is covered by ocean, but much of it is empty space (wet deserts) – middle of the Pacific Ocean is a ‘wasteland’ ­58% of modern fishes are marine ­freshwater is about 1% of overall area, only 0.01% volume; 41% of fishes are freshwater ­Only 1% move back and forth – takes a lot of effort for osmoregulation during the transition between salt­ and freshwater Properties of Water that influence Fish Functional Design 1.) Water Density – 800x denser than moving through air ­fish can be neutrally buoyant because water reduces effects of gravity ­water’s density and viscosity resists movement (pressure drag and friction drag, respectively)  development of streamlined bodies (teardrop shape) to reduce up to 95% of drag occurring on your body Ex. Bluefin Tuna – optimal design ­swim 24hrs/day (no swim bladders) 2.) Water is nearly incompressible  creates drag ­facilitates detection of vibration in water (sensory mechanisms) ­Facilitates suction feeding ­facilitates breathing with gills Water is slightly compressible  sounds travels very fast (335m/s in air vs. 1433m/s in water) ­most fish have excellent hearing (no external ears) and communicate by sound 3.) Water is universal solvent ­fish take up water with salts and organics needed to survive by feeding or by gills ­waste products also removed using gills (heat, ammonia, CO2) ­oxygen is often limiting nutrient – high surface area of gills allow them to exploit low O2 levels (8ml oxygen/1L water vs. 210ml/L water) 4.) Low Light Penetration – rarely penetrates over 100m deep Evolution of Fish The Pre­Teleost Fishes ­Fish arise from inverts via neoteny – juvenile stage becomes sexually mature and transitions into adult form ­Evolved from Tunicates (Urochordata) – pharyngeal gill slits ­Cephalo­Chordata (Amphioxus) ­possess primitive nerve chord ­no definite head or vertebrae Fish aka Craniates (includes ancestral form of all other tetrapods) Living Jawless Fish (<100extant species, very primitive) Ex. Hagfish (scavengers found on bottom) This diagram shows the juvenile features Lamprey (blood­suckers) transition into adult features, but are not lost ­no limbs altogether (e.g. proportionately large heads and short legs  Tullimonstrum gregarium (3/18/16 article) in Illinois, relative of lamprey 300MYA fossil, McCoy et al. 2016 *Evolution of Jaws was a key evolutionary innovation *Evolution of Jaw Protrusion – Important evolutionary trend among jawed fishes Gnathostomes (Jawed Craniates) ­Placoderms (extinct, many were predatory and huge) ­Sharks ­Bony fish – Lobe­finned fishes and ray­finned fishes Sharks – most primitive living jawed fishes ­full complement of fins (dorsal, pectoral, pelvic, anal fins and tail)  gives more control in 3D space ­cartilaginous skeleton Respiration in Fishes Lamprey use tidal flow (not as efficient) Sharks – use mouth or spiracles to gills Bony fish – uni­directional flow

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Chapter 5, Problem 5 is Solved
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Textbook: Single Variable Calculus
Edition: 7
Author: James W Nilsson
ISBN: 9780538497831

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Find the area of the region bounded | Ch 5 - 5, 7th Edition