Pls explain very carefully (state the thm u use in approriate part)
5. Limits of integrals Compute the following limits and justify the calculations: sin (x/n) dx
Compute the following limits and justify the calculations: a. limo*(1 (/n))-n sin(x/n) dz. c. limn-Joon sin(x/n)[x(1+x2)]-1 dr. d. limn→00 Jaon( 1 + n2x2)-1 d. (The answer depends on whether a > 0, . limn-oo a = 0, or a < 0, How does this accord with the various convergence theorems?) Compute the following limits and justify the calculations: a. limo*(1 (/n))-n sin(x/n) dz. c. limn-Joon sin(x/n)[x(1+x2)]-1 dr. d. limn→00 Jaon( 1 + n2x2)-1 d. (The answer depends on whether a...
Determine the following integrals T Sin(x) 1 + x² dx 2). xe 2x dx Idy dx + P(x) y = Q(x) integration factor Solve dy Ex dx sinx the following differenti al equations ... + 3y t? dy F) (l+x) dx +y=vx V: eSP(x) dicas
4. Evaluate the following integrals using the Residue Theorem. Justify your calculations, show the work. (10 points each) a) 12 cos a + 13 2 da b) (x2 +6x + 10)2 x sin 2x 24 13 da: c) 4. Evaluate the following integrals using the Residue Theorem. Justify your calculations, show the work. (10 points each) a) 12 cos a + 13 2 da b) (x2 +6x + 10)2 x sin 2x 24 13 da: c)
Question 5. Find the following indefinite integrals: 1. fre'de 4. .Js 3.f x In x dx 6.[(x+5) Ževæ#5dx 2. f x sin 8x dx -5 (1 + In x) sin(x Inx) dx Sin2x sin x cos x dx 5. 7. 5 2x(x2 + 4)5dx 8. dx
Evaluate the following integrals. (a) / In(3x) dx for x > 0 (e) / ( +er) dx (n lete* dx (e) sin(5x +1) dx
7. Evaluate the following integrals using integration by parts: a xe-ºrd sin (x)dx
4. Given the integrals, [° 8(x) dx =-7, 5*8(x)dx = 6 and 5*g(x) dx = 10, use the properties of integrals to determine the value of the integrals below. a) [°(f(x)+g(x)\dx b) ſ 8(x)dx (4 pts cach) c) $39(x)dx a [ f(x)dx
e" (cos(x) + sin(x) dx = e* sin(x) + C'? Justify your answer (explain how you arrived at your answer).
use residue theorem to evaluate the following integrals sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?
solve please Use symmetry to evaluate the following indefinite integrals 5 7 X - x+x dx 5 X 29. 4 2 5 +x 7 Use symmetry to evaluate the following indefinite integrals 5 7 X - x+x dx 5 X 29. 4 2 5 +x 7