Fundamental Theorem of Calculus The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of calculus, states that the integral of a function over some interval can be computed by using any one of its infinitely many antiderivatives. The fundamental theorem of calculus along curves states that if has a continuous infinite integral in a region containing…
The fundamental theorem of Calculus: The fundamental theorem of calculus asserts the interrelated properties of integration and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation. First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows, A(x)=∫_c^x▒f(x)dt, if a≤x≤b.…
1. Henri Lebesgue [8] Lebesgue is credited for many amazing discoveries to different areas of mathematics. In the area of topology, Lebesgue is known for his covering theorem which is used for finding the dimensions of a set. He is also credited for his work on the Fourier series. He was able to demonstrate that using term by term integration of a series that were Lebesgue integrable functions was always valid and therefore, gave validation to Fourier’s proof of his series. What is now…
problem given to them and their reasoning for this answer. In essence, I was hoping to target students’ knowledge of inverse functions and how they applied it to solving a situational problem. More specifically, if they were able to find the error in a solution of an inverse algebraic problem and explain their reasoning for this error. Moreover, once a student was able to state their response, I questioned their thinking and reasoning behind it in the hopes that they would use their prior…
John Gutmann was one of America’s most distinctive photographers. Gutmann was born in Germany where he became an artist. He later fled Germany due to the Nazi’s because he was a Jew. Gutmann moved to San Francisco and re-established himself as a photojournalist captivating the lives of Americans. He mainly took photographs of people who were imperfect like himself because of his Jewish nationality. Gutmann targeted the poor, circus folk, the gay community and the rich. Two of Gutmann’s works are…
Continuous Integration is a process with which the code checked-in would be verified with an automated build. This would help the developer to detect the bugs/errors in the initial phase of software development. Continuous Deployment is a methodology with which the changes are built, tested and deployed for releases. Automation is the key for DevOps. With automation DevOps enables the team to efficiently communicate, collaborate and integrate with each other. Various tools used in the…
that persons’ life form one single continuous chain, which includes beliefs, goals, and thoughts. This whole package is referred to as physiological continuity. In terms of psychological connections, the connections tend to get weaker over time as the chain of past selves/experiences grows longer (Lecture 2016). Psychological continuity and Psychological connectedness are two terms that Parfit often refers to in his explanations. Parfit believes that, “If psychological continuity took a one-many…
Materiality and Identity Megan Holmes’s “Miraculous Images in Renaissance Florence” examines many of the ramifications of materiality. The materiality, an image’s physical properties, has direct impacts on the expression and popularity of immagini miracolose. These sacred images are subjects of miracles throughout the late 13th to 16th centuries. Two of the most important ramifications of materiality include the accessibility of the religious images and manifestation of the miracles. In this…
1. What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that at least one root is a complex number? Answer: If the equation is 7th degree then it has 7 roots. Those roots can be complex or real. Complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one. This in other words, if one complex root is a + bi, then the other complex root is a – bi. If at least one root were complex, then we would have a…
II INTRODUCTION The purpose of this lab was to demonstrate and observe the effect a large focal spot and a small focal spot will have on the resolution of the image. Chapter 3 of Practical Radiographic Imaging states that resolution is “the ability to distinguish two adjacent details as being separate and distinct from each other” (Carrol, 2007, p. 48). This definition of resolution helps to explain what will be looking for to retrieve the data for this lab. As stated in Chapter 16 of…