(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.
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