(Drag and drop the missing words)Anis theof a definite integral as an endpoint of the interval of integration approaches either a specified realnumber or positive or negative. Although the integraldais, the integraldais improper. In this case, we define the improper integral as a limitdrdelimIn general, an improper integralif the limit defining itThus for exampledxdoes not.It is possible for an improper integral toto infinity. For instance,00 drdr= limC00isHowever, there are many improper integrals which diverge in no particular direction, such asz sin zdroscillatesinfinitydivergedivergentRiemann integralinfinite integralexistsconvergedefinite integralimproper integrallimitconvergesnot improperzero一”

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Answered: (Drag and drop the missing words) An is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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True or False Plus. A. Any function cannot be integrated from limits a to b where c is a discontinuity given that a<c<b. B. Any improper integral not converging to a single value as an answer is considered diverging. Choices A. Both A and B is true B. Both A and B is false C. A is true, B is false D. A is false, B is true
f(x) =√(x3+ 8) a) Use properties of the integral and show that 3 ≤ 1∫2 f(x)dx ≤ 4 b) Express the integral 1∫2 f(x)dx as a limit of a Riemann sum. Do not evaluate the limit.
EMERGENCY Which one is correct? f(x) is not continuous at x=0. f(x) has no limit as x approaches zero. f(x) is continuous on the set of real numbers. f(x) is continuous at x=1 f(x) is right continuous at x=0 but not left continuous there.
Subject: Improper integrals. Note: Use limits (Lim) taking into account the subject matter of the guide book (stewart 7 edition) section 7.8. 1. Determine a value of n for which the improper integral. Figure 1 Let it be convergent and evaluate the integral for this value of n.
Part A Decide whether the integral in the picture is improper. Explain your reasoning by chosing one of these choices a)The integral is improper because the upper limit of integration is infinite. b)The integral is improper because the lower limit of integration is infinite. c)The integral is improper because both the upper limit of integration and the lower limit of integration are infinite. d)The integral is proper. e)The integral is improper because the function has an infinite discontinuity in [6, 13]. Part B Determine whether it diverges or converges. Part C Evaluate the integral if it converges. (If the quantity diverges, just say DIVERGES.)
Real Analysis Is the proof for this claim correct? State that it is correct, or circle the first error you see if it isn't, and explain if it can be corrected to be proven true. Claim: If f: [a,b] → R is continuous and not constant, then its range is a closed, bounded interval. Proof: Since f is continuous on a compact domain, its range is compact and hence closed and bounded. Since the range is bounded, it has a supremum and an infimum. Since the range is also closed, the supremum and infimum belong to the range. Therefore the range is the closed and bounded interval [m,M], where m is the infimum and M is the supremum of the range.
An unknown constant Let a. Determine the value of a for which g is continuous from theleft at 1.b. Determine the value of a for which g is continuous from theright at 1.c. Is there a value of a for which g is continuous at 1? Explain.
Consider the function f(x)=2x on the interval [0,10]. Let P be a uniform partition of the interval with n sub-intervals.a) Express the right Riemann sum as a function of n.Right-Sum: b) Compute the limit of the right-sum you found as n approaches infinity.L= c) Compute the definite integral using the antiderivative. Make sure you show all steps and use correct notation. 0∫10 2xdx d) Draw a picture and use geometry to find the same integral as area under the graph
WORK THROUGH ALL INTEGRALS WORK THROUGH ALL LIMITS INTEGRATE BY TRIG SUBSTITUTION
(Comparison Theorem) Use the Comparison Theorem to determine if the following integralconverges or diverges. Show all work and justify your conclusion. Thank you! (This is from james stewart)
Calculus Let the region R be the area enclosed by the function f(x)= √x + 2the horizontal line y=5, and the y-axis. Write an integral in terms of x and also an integral in terms of y that would represent the area of the region R. If necessary, round limit values to the nearest thousandth. Please determine x1 , x2 , y1 , & y2 .
handwritten solution is better please write legibly. (a). Find all possible points of discontinuity. Then determine if f is continous on every point og discontinuity. (b). Classify each discontinuity as removable, jump essential, or infinite essential. If removable discontinuity, redefine the function. **This is continuity of limits. please avoid using integrals or derivatives.

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