7. Evaluate ſe cos x dx. 8. Is the series 2 (-)" convergent or divergent? Prove...
(-1)-1 n2 is absolutely convergent. 1. (2 points) Prove that cos n is convergent or divergent. 2. (2 points) Determine whether the series - (Use cos n<1 for all n) 3. (3 points) Test the series -1) 3 for absolute convergence. (Use the Ratio Test) 2n +3) 4. (3 points) Determine whether the series converges or diverges. 3n +2 n-1 (Use the Root Test) 5. (3 points) Find R and I of the series (z-3) 1 Find a power series...
Is the following series cos n convergent or divergent? Prove your result. 2 if Σ an with an > o is convergent, then is Σ a.. always convergent? Either prove it or give a counter example. 3 Is the following series convergent or divergent? if it is divergent, prove your result; if it is convergent, estimate the sum. 4 Is the following series 2n3 +2 nal convergent or divergent? Prove your result.
Use the Integral Test to determine whether the series is convergent or divergent. ∞ n n2 + 8 n = 1 Evaluate the following integral. ∞ 1 x x2 + 8 dx Since the integral finite, the series is . Use the Integral Test to determine whether the series is convergent or divergent. n2 8 Evaluate the following integral. OO dx Since the integral ---Select--- finite, the series is ---Select---
Is the following series convergent or divergent? If it is convergent, then evaluate what the series converges to. noor(n+1)ī (sin?(x)) Zn=1Jnt I dx
Use the Integral Test to determine whether the series is convergent or divergent. ∞ n n2 + 2 n = 1 Evaluate the following integral. ∞ 1 x x2 + 2 dx
1. Consider the series n=2 Is it divergent, conditionally convergent or absolutely convergent? Explain. 2. Suppose you know that 2n+1 sin(x) = Ž (-1)" 2** * Explain how to use this to show that cos(x) = ŽC-1) HINT: What is sin(x)?
Determine whether the integral is convergent or divergent. integral_-infinty^0 1/3 - 4x dx convergent divergent If it is convergent, evaluate it. (If the quantity diverges, enter diverges.) Determine whether the integral is convergent or divergent. integral_8^infinity 1/x^2 + x dx convergent divergent If it is convergent, evaluate it. (If the quantity diverges, enter diverges.) Determine whether the integral is convergent or divergent. integral_-2^14 5/4 squareroot x + 2 dx convergent divergent If it is convergent, evaluate it. (If the quantity...
Use the Integral Test to determine whether the series is convergent or divergent. ne-n n = 1 Evaluate the following integral. dx Since the integral --Select--- finite, the series is ---Select---
Determine whether the integral is convergent or divergent. 0 34 e1/x x3 dx −1 convergent divergent If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) 6 + -1 points SCalcET8 7.8.039. 013 Submissions Used Determine whether the integral is convergent or divergent. 1034 1/x convergent divergent If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)
Determine whether the following series is absolutely convergent, conditionally convergent, or divergent. (–1)n-1((In n) 2n (3n+4)n • State the name of the correct test(s) that you used to reach the correct conclusion. • Show all work. • State your conclusion.