Continuous function

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…

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…

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…

the equation & based off what I did I'm assuming that his possible answer came out not to be an real answer to his problem & that is mainly because the equation itself is not true when eighty one is inserted for the letter x in the default problem. Okay so basically for this particular problem we have to think of f of x as basically the y value if that makes sense. So this would mean that if you use addition for the number two & + to the letter y we will see the function go up by two. The…

Story evaluation The story that will be evaluated is one entitled “Man was paid $2 500 to conceive a child with his neighbor’s beauty queen wife, but failed after 3 months trying”. Firstly, there is doubt in the story due to the source which is responsible for sharing the news. The source is a website known as 9GAG, which does not have any reputable evaluation system, and anyone is free to post a story he or she wants. However, judging by the comments on the post, many individuals assume the…

Intervention Description Joint Protection (JP) is a strategy for performing activities to minimise the amount of strain and pain throughout the joints being used (Goodacre & McArthur, 2013). Common barriers clients face when applying JP strategies are; information memorisation, fear of appearing disabled and the unwillingness to change lifelong habits. Studies indicate that addressing these barriers is imperative for increasing the effectiveness of JP (Hammond et al, 1999) (Niedermann et al,…

Furthermore a 4-6 month rehabilitation plan was prescribed following surgery to reduce pain, limit swelling, restore range of motion (ROM), and regain maximal function. The patient hopes to resume full basketball activity within 6 months post surgery and to prevent…