In the following exercises, compute the average value using the left Riemann sums \(L_{N}\) for N = 1, 10, 100. How does the accuracy compare with the given exact value?

[T] \(y=x \sin \left(x^{2}\right)\) over the interval \([-\pi, 0]\) ; the exact solution is \(\frac{\cos \left(\pi^{2}\right)-1}{2 \pi}\).

Text Transcription:

L_N

y=x sin (x^2)

[-pi, 0]

cos (pi^2)-1/2 pi

Developmental biology – Week 1 Modern developmental biology studies the genetic control of cell growth, differentiation and "morphogenesis," o which is the process that gives rise to tissues, organs and anatomy. Embryology is a subfield, the study of organisms between the one-cell stage (generally, the zygote) and the end of the embryonic stage. Embryology and developmental biology today deal with the various steps necessary for the correct and complete formation of the body of a living organism. The term biology is derived from the Greek word βίος, bios, "life" and the suffix -λογία, -logia, "study of. o The Latin-language form of the term first appeared in 1736 when Swedish scientist Carl Linnaeus (Carl von Linné) used biologi in his Bibliotheca botanica. o It was used again in 1766 in a work entitled Philosophiae naturalis sive physicae: tomus III, continens geologian, biologian, phytologian generalis, by Michael Christoph Hanov, a disciple of Christian Wolff. o The first German use, Biologie, was in a 1771 translation of Linnaeus' work. In 1797, der Lehre van der Lebenskraft.d the term in the preface of a book, Grundzüge o Karl Friedrich Burdach used the term in 1800 in a more restricted sense of the study of human beings from a morphological, physiological and psychological perspective (Propädeutik zum Studien der gesammten Heilkunst). o The ter