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5865. Completing the square Evaluate the following integrals. L x2 +

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 62 Chapter 7.4

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 62

5865. Completing the square Evaluate the following integrals. L x2 + 2x + 4 2x2 - 4x dx, x 7 4

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Lecture 30 Details of Development Overview  4 key stages to animal development: o Fertilization o Cleavage o Gastrulation o Organogenesis  Mechanics of morphogenesis o Cell fates o Development of body axes o Limb development Fertilization Leads to Pregnancy and Temporary Disruption of the Cycles  Fertilization (“conception”): sperm fuses with mature oocyte in oviduct o 24 hours: first cleavage (deuterostomes, radial) o 2-3 days zygote reaches uterus o 1 week: blastocyst (hollow ball of cells), implants in endometrium o Develops into fetus  Embryo produces hGC (human chorionic gonadotropin) o Works like LH to keep corpus luteum from degrading o Keeps progesterone levels up o hGC can be detected in mother’s urine; pregnancy test  Pregnancy: one or more embryos in the uterus Most Developmental Work is Done with Species Other Than Humans  We must rely on model organisms o Fruit fly: Drosophila melanogaster o Sea urchin: various species, e.g., Strongylocentrotus purpuratus o Frog: Xenopus laevis o Chick: Gallus gallus o Nematode: Caenorhabditis elegans  A good model organism is one that is: o Cheaply available or can breed in the lab o Has properties that make it useful for studying some biological process o From a species that we don’t mind killing Development of a Zygote Begins at Fertilization  Fertilization: union of sperm and egg o N + N = 2n o Best studied in sea urchins; external fertilization  Unfertilized egg o Plasma membrane with receptors o Vitelline layer: extracellular matric o Jelly coat: protects egg and attracts sperm  Contact triggers acrosomal reaction o Acrosome: vesicle at sperm tip with hydrolytic enzymes break down jelly o Acrosomal process: structure with proteins that bind receptors on eggs  Matching receptors ensures sperm matches egg o Fusion of plsma membrane o Depolarization: fusion leads to change in membrane potential  Fast block to polyspermy Fertilization is a Process, Not an Event  Fusion also initiates cortical reaction o Vesicles in cortex (outer part) fuse with plasma membrane o Contents (enzymes, etc.) lead to fertilization envelope and slow block to polyspermy  Separate vitelline layer from plasma membrane  Breaks up receptors  Following cortical reaction, the egg is “activated” o Increased respiration & protein synthesis o Sperm nucleus fuses with egg nucleus o First cell division after 90 minutes  Mammal fertilization basically the same, except: o Internal fertilization o No fast block to polyspermy o Egg completes meiosis II after fertilization o First cell division after 12-36 hours Cell Divide to Form a Blastula  Cleavage: earliest divisions, rapid o Cells divide, but don’t grow o Blastomeres: individual, cells  Blastula: hollow ball of cells with a blastocoel  Relatively simple in sea urchins The Body’s Polarity is Established from the Beginning of Cleavage  Development of body polarity is well-studied in frogs o Because parts of zygote are color-coded; easy to follow  Even before fertilization, oocyte not just an unorganized blob o Cytoplasmic determinants: proteins, mRNA, etc. in various places o Yolk: stored nutrients  Two poles that determine first divisions o Yolk concentrated toward the vegetal pole o Opposite: animal pole  Some polarity set a fertilization o Animal vegetal axis  anterior posterior axis o Area opposite sperm entry (gray crescent)  dorsal  Cortical rotation  Presence of yolk influences shape of blastula o First 2 divisions, lead to 4 blastomeres o 3 division: 8 cells; unequal offset by yolk o Blastocoel only in animal hemisphere Gastrulation is the Process by Which Adult Germ Tissues Are Formed  During gastrulation the ball of cells turns into a structure with 2-3 tissue layers and a gut (gastrula) o Mass movement of cells  For a sea urchin, this is exactly the process we have already talked about o Three tissues (germ layers) are ectoderm, endoderm, and mesoderm o Starts at vegetal pole  Migratory future-mesoderm cells enter blastocoel  Other cells (future-endoderm) form vegetal plate  Vegetal plate invaginates and becomes archenteron  Opening is the blastopore: future-anus (deuterostome) Gastrulation is More Complex in a Frog Because of all the Yoke  Slit-like blastopore forms on dorsal side; extends around entire blastula  At same time, future-endoderm and – mesoderm expand by involution; shrinks blastocoel  End of gastrulation, blastopore surrounds yolk plug All This is Slightly More Complicated in Birds by the Large Amount of Yolk  In the chicken, disk of blastoderm forms as two layers of cells on a large yolk o Hypoblast on near yolk, epiblast on top  Gastrulation by migration of epiblast cells toward yolk; forms primitive streak (- blastopore) o Future endoderm forms archenteron thru lateral folds pulling away from yolk  Organogenesis as in frog, except for the presence of extraembryonic membranes o Chorion: gas exchange o Amnion: encloses embryo in fluid o Yolk sac: surrounds yolk o Allantois: sequesters waster produts o All formed of embryonic tissues Among Eutherian Mammals, Nourishment From the Yolk is Replaced With Nourishment From the Mother  Because nourished by mother, eutherian eggs can be smaller: no need for bulky yolk o Rest of process similar to birds o Best studied in mice and early stages of human in vitro fertilization  Cleavage to 8-blastomere stage: 3 days o After six days, ready to implant in uterus; > 100 cells  1. Blastocyst: mammalian blastula o Trophoblast: outer epithelium o Inner mass calls: part that will become the embryo  2. Trophoblast initiates implantation o Secretes enzymes to break down endometrium o Thickens, sends extensions to maternal blood vessels o Inner mass cells from epiblast and hypoblast  3. One implanted, gastrulation initiated & embryonic membranes form o Placenta derived from trophoblast, mesoderm from the epiblast, and endometrial tissue  4. Three layered embryo with 4 extraembryonic membranes The Human Gestational Period is Typically 38 Weeks  First 2-3 weeks: embryo gets nutrients directly from endometrium  Placenta forms from embryonic and material tissue; blood vessels from both exchange nutrients, gases, wastes, etc.  After 8 weeks of organogenesis, embryo termed a fetus Morphogenesis is Cells Changing Shape and Moving Relative to Each Other  Animal cells change shape using cytoskeleton o E.g., formation of neural tube  Microtubules elongate cells  Perpendicular microfilaments narrow the apex: make cell wedge-shaped  Animal cells move using cytoskeleton o Crawl much like an amoeba  Cells form stable tissues using cell adhesion molecules (CAMs); usually glycoproteins on cell surface o Allow cells to recognize others and bind them with specific receptors  Migration of cells also mediated by extracellular matrix: mesh of macromolecules outside of cells o Migrating cells have receptors that bind matrix and neighboring cells to control where they are suppose to be  Different cells have specific receptor proteins What is the Genetic Basis of all this  All cells have the same genes, but different cells have different structures and functions o Depends on which genes are expressed at what time  How do we think this works o 1. As cleavage proceeds, cells differentiate  Starts with asymmetrical distribution of cytoplasmic determinants  Dividing it up leads to different cells  Specify body axes, gene expression, etc. o 2. Once asymmetries set up, further differentiation depends upon interactions between cells  Induction: changes in gene expression based upon such interactions  Cell-cell contact and/or signaling molecules As Cell Lines Develop, they Become More Locked into Specific Roles  C. elegans: nematode that is very useful for studying the diversification of cells o Small, lives well in the lab o Every adult has exactly 959 cells  Can make a fate map of cell differentiation by: o Watching cells divide o Destroy certain cells and see what doesn’t develop  Conlusions: o Older cells are always derived from certain cell lines with unique factors o As cell lines develop, they lose their developmental potential: they can become fewer different types of cells Animals Differ in the Timing of Losing Their Developmental Potential  Frog body axes set by distribution of yolk & location of fertilization o Animal vegetal, anterior posterior o Sperm entry gray crescent, ventral dorsal o Left and right by default  Among amniotes, polarity not set so early o Body axes can depend on initial orientation of sperm and egg o E.g., mammal cells remain totipotent until 16-cell stage: at 8-cel stage, each blastomere can still become an embryo  However, even in mammals eventually cells lose developmental potential o Once they are different they can interact with each other: induction Pattern Formation is Controlled by Induction  Induction is involved in pattern formation by providing positional information o E..g, limb development in a chick  Limbs begin as mesodermal limb buds, covered in layer of ectoderm; three axes o Proximal distal: shoulder to finger o Anterior to posterior: thumb to pinkie o Dorsal ventral: knuckle to palm  As with growth factors in plants, positional information comes from gradients  Two important organizer regions o Apical ectodermal ridge (AER): at tip of bud  Secretes growth factor that extends limb bud o Zone of polarizing activity (ZPA): posterior, proximal location  Organizes anterior posterior development: furthest become anterior  Experimentally ass anterior ZPA: get “mirrored” limb

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Chapter 7.4, Problem 62 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. Since the solution to 62 from 7.4 chapter was answered, more than 231 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 128 chapters, and 9720 solutions. The full step-by-step solution to problem: 62 from chapter: 7.4 was answered by , our top Calculus solution expert on 12/23/17, 04:24PM. The answer to “5865. Completing the square Evaluate the following integrals. L x2 + 2x + 4 2x2 - 4x dx, x 7 4” is broken down into a number of easy to follow steps, and 21 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2.

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5865. Completing the square Evaluate the following integrals. L x2 +