Calculus
1 Hour Exam 3 (continued) - Math 220
Fall, 2011
6. |
Fill in the missing information for the following theorem. Rolle’s Theorem: Let f be a function that satisfies the following three hypotheses: 1. F is continuous on the closed interval [a,b] 2. F is differentiable on the open interval (a,b) 3. _____________________________________ Then there is a number c in (a,b) such that ___________________________. Answer: 3. f(a) = f(b) such that f’(x) = 0 |
7. |
If Newton’s Method is used to approximate a solution to the equation f(x) = 0, then it generates a sequence of approximations x1, x2, x3, . . . Which one of the following relations correctly shows how xn can be used to determine the next approximation xn+1 ? a. xn+1 = [xn + f’(xn)] / f(xn) b. xn+1 = xn + f’(xn) / f(xn) c. xn+1 = [xn + f(xn)] / f’(xn) d. xn+1 = xn + f(xn) / f’(xn) e. xn+1 = [xn - f’(xn)]/ f(xn) f. xn+1 = xn – f’(xn) / f(xn) g. xn+1 = [xn - f(xn) / f’(xn) h. xn+1 = xn - f(xn) / f’(xn) Answer: h |
8. |
Fill in the missing information to show that the given definite integral can be expressed as the limit of a Riemann sum. The only variables appearing in your limit should be n and k. You do not need to evaluate this limit. 6 n ∫ (x5 + 8)4 dx = lim Σ [ ] 2 n→∞ k=1 Answer: ( ( ( 2 + k (4/n) )5 + 8 ) (4/n) Click here to continue with this exam. |