(a) Set up the appropriate limit(s) to evaluate the improper integral Do not evaluate the limit(s)....
a) Set up the appropriate limit(s) to evaluate the improper integral Do not evaluate the limit(s). Ś 4. 12 - 31 dr. (b) Determine whether the following integrals is proper, improper and convergent, or improper and divergent. Justify your answer. x + arctan(a) x + 3 $ (c) Evaluate the following integral or determine whether it is convergent. 1 S Edi X-V
i. Explain why this definite integral is an improper integral. ii. Determine if this improper integral converges or diverges. Be sure to treat the improper integral with appropriate mathematical rigour. Simply treating the improper integral as if it was a proper integral will result in zero marks. Furthermore, make sure you clearly explain/justify each step in your limit analysis working. thanks for your answer, please give a clear writing. (b) Consider the definite integral 2 1 i. Explain why this...
4. (a) Indicate where the series is (i) absolutely convergent, n-1 where it is (ii) conditionally convergent, and where it is (iii) divergent. Justify your answers Find f,(z) if f(x) = arctan (e* ) + arcsin V2x + 4. (b) (a) Set up (but do not evaluate) a definite integral that represents the area 5. of the region R inside the circle r = 4 sin θ and outside the circle r = 2. Carefully sketch the region R. (i)...
Determine whether the improper integral is convergent or divergent. 18 s dx (x + 1)2 2 Divergent O Convergent
Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your sample points.) 6 x 1 + x4 dx 4 lim n → ∞ n i = 1 arctan(36)−arctan(16)2 ❌ Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your sample points.) to it yox arctan(36) - arctan (16) Need Help? Read Watch Master It...
Write the following improper integral as a limit of definite integrals, or as a sum of limits of definite integrals. DO NOT EVALUATE IT. (11/2 (tan/ode
em #6: Evaluate the following improper integral. 1, 63-2033 die If the integral does not converge, then write "divergent" (without the quotes). Problem #6: Enter your answer symbolcally as in these examples If the integral does not converge, then write "divergent". Problem #8: Which of the following graphs is the level set of corresponding to (6)
x-5 dx. ) Evaluate the definite integral S 22-3x+2 Determine whether the improper integral S, dx converges. If convergent, find its value.
Given the improper integral 1 = ( (v + 2)(5 – 3' dr, which of the following is correct? Convergent, I = In 3 Convergent, I = In 2 Convergent, 1 = In Divergent Convergent, I = In 6
(b) For which s E C does the integral dr exist as an improper Riemann integra? Justify your answer. (e) Evaluate J(s) by considering a contour integral around a suitably chosen rectangular contour (a) tse a value of s for which J(s) can be evaluated by elementary means to check your answer to part (e) (e) Use your answer to part (e) to evaluate cos(anld (where a E R). (f) Hence (where α E R) determine the value of (...