Use the Limit Comparison Test to determine convergence or divergence. Σ 8n²+n+1 4 n = 1 n²+6n²-3 Select the expression below that could be used for b in the Limit Comparison Test and fill in the value of the limit L in your choice. O bn 1 gives L = 2 n 1 ○ bn = gives L = n O bn = n gives L = Obn√√n gives L = Does the series converge or diverge? Choose the correct answer below. O Diverges O Converges

Find the indicated trapezoid approximations to the following integral. 18 5x² 5x dx using n = 2, 4, and 8 subintervals T(2)=(Simplify your answer. Type an integer or a decimal.) T(4) = (Simplify your answer. Type an integer or a decimal.) T(8)=(Simplify your answer. Type an integer or a decimal.)

← Use the Integral Test to determine whether the following series converges after showing that the conditions of the Integral Test are satisfied. Σ √k+2 k=0 7 Determine which conditions of the Integral Test are satisfied by the function f(x)= Select all that apply. √x+2 A. The function f(x) is continuous for x≥0. B. The function f(x) has the property that a = f(k) for k = 0, 1, 2, 3, C. The function f(x) is positive for x≥0. D. The function f(x) is an increasing function for x≥0. E. The function f(x) is a decreasing function for x≥ 0. F. The function f(x) is negative for x ≥0. Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. 00 The series diverges. The value of the integral 7 dx is √x+2 OB. (Type an exact answer.) The series converges. The value of the integral (Type an exact answer.) OC. The Integral Test does not apply to this series. 0 7 dx is √√x+2

Evaluate the following integral or state that it diverges. 8 S 8 2xe-5x2 dx Select the correct choice and, if necessary, fill in the answer box to complete your choice. 8 OA. The integral converges and S 2xe-5x2 dx = (Type an exact answer.) OB. The integral diverges.

Evaluate the following integral. 19 sin 3 19 sin x cos 2x dx 19 sin 3 2 x dx = ☐ 19 sin x cos x dx

I need detailed help solving this exercise from homework of Calculus I.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!---------------------------------------------------------------------------------Part 3: Fill-in-the-Blank Questions

I need detailed help solving this exercise from homework of Calculus I.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!---------------------------------------------------------------------------------Part 1: Multiple-Choice Questions, Each Problem with Single Correct Answer

I need detailed help solving this exercise from homework of Calculus I.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!---------------------------------------------------------------------------------Part 1: Multiple-Choice Questions, Each Problem with Single Correct Answer

I need detailed help solving this exercise from homework of Calculus I.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!---------------------------------------------------------------------------------Part 2: Multiple-Choice Questions with More Than One Correct Answers