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(a) Find a positive continuous function f such that the

Calculus | 8th Edition | ISBN: 9781285740621 | Authors: James Stewart ISBN: 9781285740621 127

Solution for problem 1 Chapter 6

Calculus | 8th Edition

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Calculus | 8th Edition | ISBN: 9781285740621 | Authors: James Stewart

Calculus | 8th Edition

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Problem 1

(a) Find a positive continuous function f such that the area under the graph of f from 0 to t is Astd t 3 for all t . 0. (b) A solid is generated by rotating about the x-axis the region under the curve y fsxd, where f is a positive function and x > 0. The volume generated by the part of the curve from x 0 to x b is b2 for all b . 0. Find the function f.

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Lecture Notes March 9 , 2016 Reproduction and Development  Anatomy and Physiology o Gametogenesis- the production of gametes  Spermatogenesis- production of sperm- in the testes located in a sack like structure called the scrotum- occurs continuously throughout a male’s reproductive life  Testes have two functional components o Seminiferous tubules- where the sperm is produced o Interstitial Cells- secrete the male sex hormone- testosterone  During spermatogenesis the cells lining the seminiferous tubules are called 1° spermatocytes (2N)  2° spermatocytes (N)  become spermatids ----differentiation (lose cytoplasm and grow tail) Sperm (Spermatozoa)  Sperm have little food reserve and die within 72 hours, but in very low temperatures they can survive for years  Men must release 100 million sperm during intercourse to be considered fertile- some men release 1 billion per ejaculation  Oogenesis- production of eggs in the ovaries- suspended in the abdominal cavity  Two functions of ovaries o Produce the oocytes o Secrete female sex hormones- estrogen and progesterone  Begins before the female is born o Oogonia 1° oocytes (2N) (born with 3-400K) 2° oocytes o Happens once a month only one created  During cytokinesis one of the two cells formed during meiosis gets less cytoplasm- polar body 1  Secondary oocytes are in a sack structure called the follicle  At puberty ovaries begin to release one 2° oocyte every 28 days- ovulation  Ovulation begins when a follicle near the surface of the ovary begins to grow and fill with fluid  Eventually the pressure inside the follicle becomes so great that it ruptures and the 2° oocyte is released into the abdominal cavity  Meiosis II only occurs if the 2° oocyte is penetrated by a sperm  During Meiosis II another polar body is formed- three of the four eggs disintegrate  Once the true egg is formed- fertilization can take place and the zygote 2N is formed Lecture Notes  Since the female has been carrying 1° oocyte for many years the chances that mutations have occurred is much higher than for male sperm o Of the 3-400K oocytes only 13 are ovulated each year o Not very many are released throughout a females life and they will all disintegrate around the age of 50 o Male Reproductive Tract  A coiled tube called the epididymis lies on the surface of the testes and carries the sperm to the vasteferens  That’s what gets cut when you have a vasectomy  Vasteferens (2) run into the abdominal cavity and join the urethra just beyond the point where it leaves the bladder  The urethra passes through the penis and empties to the outside  As the sperm passes through the vasterferens and the urethra seminal fluids added to form semen (seminal fluid + sperm = semen)  Seminal fluid is produced by three glands o Seminal vesicles o Prostate o Cowper’s  Seminal Fluid has four main functions o Vehicle for the transport of sperm o Lubrication of passages o Chemical buffer against the acids in the female reproductive tract o Contains sugars- provide sugars which provide energy to the sperm o Female Reproductive Tract  From the ovary 2° oocyte travels through the abdominal cavity and is swept into the oviduct/ fallopian tube  The swept down the fallopian tube into the uterus  Uterus- pair shaped and muscular  If 2° oocyte is entered by a sperm meiosis II occurs, egg is fertilized and implants on uterine wall  If egg is not penetrated it passes through the cervix into the vagina during menstruation

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Textbook: Calculus
Edition: 8
Author: James Stewart
ISBN: 9781285740621

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(a) Find a positive continuous function f such that the