Help on number 2 A-C Math 166 Spring 2020 Lab 12 - Integration Strategies and Improper...
Question 2 please 1 and 2, determine whether or not the integral is In exercises improper. If it is improper, explain why 12. (a) 12 x-2/5 dx 「x-2/5 dx 「x2/5 dx (b) (c) I. (a) 0 13. (a 40 1 dx 2 x 14. (a In exercises 3-18, determine whether the integral converges or diverges. Find the value of the integral if it converges. 15. (a (b)人1x-4/3 dr 3, (a) l.lyMdx (b) x43 dx 16. (a 4. (a) 45 dx...
(b) (5 points) Determine if the following improper integral converges or diverges: de √x-2 (C) (5 points) Prove that the improper integral do is converging.
How to prove this theorem hold? (It is an improper integral, extension of Riemann) SKT 6:01 Theorem lI Let f(x, y) be continuous for a s x 00, c s y 00, and let the integrals J(y)dr f(x, ) and J ( dy f(x, z) be respectively, uniformly convergent on every finite interval c sy
(1 point) Call an improper definite integral type 1 if it is improper because the interval of integration is infinite. Call it type 2 if it is improper because the function takes on an infinite value within the interval of integration. Classify the type(s) for each of the following improper integrals. ? 1. sec(x) dx 0 ? 2. $x2-3x+6° x2 - 5x + 6 1 ? 3. Loints dx -00 x2 00 ? 4. dx
Graphs of functions and are shown below. Suppose x = 0 and x = -1 are vertical asymptotes for both functions. Assume that the graphs continue in the same way as x approaches a 0 and 4(eg stays on top close to = 0, and stays on top close to-). Which of the following statements is TRUE? g(x) f(x). -3 O If 9(x) dx converges, then dar converges too. Isla) na ſs) dx either both 0 The integrals 9(2) dar...
We have the following Limit Comparison Test for improper integrals: Theorem. Suppose f(x), g(x) are two positive, decreasing functions on all x > 1, and that lim f(x) =c70 x+oo g(x) Then, roo 5° f(x) dx < oo if and only if ſº g(x) dx < 00 J1 (a) Using appropriate convergence tests for series, prove the Limit Comparison Test for improper integrals. (Hint: Define two sequences an = f(n), bn = g(n). What can you say about the limit...
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
This problem is concerned with evaluating some improper integrals. In particular you will use an improper integral over an interval of infinite length to evaluate an integral of a function not defined at one end point. This will involve a special function「which arises in many applications in the sciences. a. Evaluate Jo (log z) dr. b. Explain how you would evaluate Jr*(log x)7 dr, but do not actually compute it. Would your method work if the exponent'8, were replaced by...
the selections are the same for all three In each case determine if the given information can be used to prove that the improper integral converges or diverges. If it is impossible to tell from the information, select inconclusive. Assume that the function has no other discontinuities or hidden features on the interval of integration. Then include your reason for your answer. Be specific. (a) Information: lim f(x) = 60 X-5 18 What can you say about L'oro f(x) dx?...
can you solve for me the exercises 2 in class I need all of these please thank you so much Exercise 10. Show that J dz converges. Class Exercise 2. Use integration, the direct comparison test, or the limit comparison test to determine whether the integral converges or diverges. tan 6 de x/2 (a) a (b) 2re- (e) fo (d) (e) Jo (f) (s) dr dt vt+sint dr +1 da 1-2 1 de 1+e dr Foo 2+cosz dr (h) ()...