Let a, b = R. Let f : [a, b] → R be an integrable function. Let g: [a, b] → R be a function which agrees with f at all points in [a, b] except for one, i.e. assume there exists a c = [a, b] such that g(x) = f(x) for all x = [a, b]\{c}. And g(c) < f(c). Prove that g is integrable on [a, b] and that fog(x)dx = So f(x)dx. Hint: Prove that g(x) - f(x) is integrable and the integral is 0.

Let a, b = R. Let f : [a, b] → R be an integrable function. Let g: [a, b] → R be a function which agrees with f at all points in [a, b] except for one, i.e. assume there exists a c = [a, b] such that g(x) = f(x) for all x = [a, b]\{c}. And g(c) < f(c). Prove that g is integrable on [a, b] and that fog(x)dx = So f(x)dx. Hint: Prove that g(x) - f(x) is integrable and the integral is 0.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A national study found that treating people appropriately for high blood pressure reduced their overall mortality by 20%. Treating people adequately for hypertension has been diffcult because it is estimated that 50% of hypertensives do not know they have high blood pressure, 50% of those who do know are inadequately treated by their physicians, and 50% who are appropriately treated fail to follow this treatment by taking the right number of pills. Answer the following questions ( please answer all the parts 1,2 and 3): 1) What is the probability that among 10 true hypertensives at least 50% are being treated appropriately and are complying with this treatment?2) What is the probability that at least 7 of the 10 hypertensives know they have high blood pressure? 3) If the preceding 50% rates were each reduced to 40% by a massive education program, then what effect would this change have on the overall mortality rate among true hypertensives; that is, would the mortality rate decrease…
answer part 2 frq styed please and show work 1. Because of the constantly evolving political climate around the United States, Gallup (who regularly conducts polls in the U.S.) conducted a poll just after the inauguration asking U.S. adults if they approve of the initiatives President Biden had implemented in his first few days in office. Another Gallup poll was conducted now that President Biden has been in office for a month asking U.S. adults if they approve of the initiatives President Biden had implemented after his first month in office. According to the first Gallup poll of 1500 randomly selected U.S. adults, 64% approved of the initiatives President Biden had implemented in his first few days in office. And according to the second Gallop poll of 1700 U.S. adults, 54% approved of the initiatives President Biden had implemented after his first month in office. Construct and interpret a 95% confidence interval for the change (difference) in the true proportion of U.S. adults…
Whiat would be a easy suitable research design for this topic. Topic: The impact of unemployment on mental health in Anguilla.
As a prospective teacher, communication skills occupy a very important position, because communication skills will affect the understanding of the students they teach. With good communication skills, a teacher can convey his ideas or ideas well, on the other hand, if his communication skills are not good, the ideas or ideas will not be conveyed perfectly. Communication skills provide opportunities for students to convey their ideas both verbally and in writing and learn to respect the opinions of others. Communication is a process of giving and conveying meaning in an effort to create mutual understanding. Communication is a process, not a static thing, so communication. Students from well-known universities in Jakarta are students who are prepared to become prospective teachers in elementary schools. Thus, these students need to be prepared and trained from an early age to develop communication skills. This is because to form students with good communication skills requires a long…
What is a dummy variable trap and how is it related to multicollinearity of regressors? What is the solution for this form of multicollinearity?
Currently studying for exams and am really stuck on this practice problem. Please help with question 7 and 8 by providing detailed solutions, thank you.
PLEASE HELP
State and explain the significance of the three basic principles of experimental design.
Please help me with these 2 questions.Help is very much appreciated!!
Please answer all parts of the question, thank you