Calculus 2:

Chapter 6 Review: Problem 1 (1 point) The differentiation rule that helps us understand why the Substitution rule works is: A. None of these B. Both rules OC. The chain rule OD. The product rule.Chapter 6 Review: Problem 10 (1 point) YOU want to estimate the area underneath the graph of a positive function by using sutHntervals Of equal Width. Check each True statements below: DA. "0 use the Simpson's rule, an even number of rectangles must be used D B. "he absolute value of the Mldpoints estimate is half of the absolute value of Trapezoid Rule estimate D 0. "he Midpoint estimate is the average of the Le and Right endpoints estimates D D. For an increasing function the Left endpoints estimate is an underestimate and the Right end points estimate is an overestimate. D E. 'he absolute value ofthe error of the Midpoints estimate is about halfofthe absolute value of the error of the Trapezoid Rule estimate Chapter 6 Review: Problem 2 (1 point) The differentiation rule that helps us understand why the Integration by Parts rule works is: OA. The chain rule. B. None of these OC. Both rules OD. The product ruleChapter 6 Review: Problem 3 (1 point) Given that fo f(x) dx = 2, check all integrals that are possible to find: A. None of these OB. fo 2f(x)dx Oc. fo 2f(x)dx OD. fo f(2x ) dx DE. fo f(2x)dxChapter 6 Review: Problem 4 {1 poin The best way to evaluate I23 - En[m)dz is by using |:| A. Partial Fraction Decomposition I] B. None of these I] C. Integration by Part5 |:| I]. Substitution Chapter 6 Review: Problem 5 {1 peintJ The best substitution to evaluate I 3 rim is 23! [111.12 253$ DELI: 21';an DC.:I:= 2311113 [J I}. None [If these Chapter 6 Review: Problem 6 (1 point) To evaluate | 7 9 x we can use A. Only Trigonometric Substitution r = 3sect B. Both, Trigonometric substitution or Partial Fractions C. None of these OD. Only Partial Fraction Decomposition DE. Only Integration by PartsChapter 6 Review: Problem 7 (1 point) The best way to evaluate [ t2 . edt is by using DA. None of these OB. Integration by Parts OC. Substitution OD. Partial Fraction DecompositionReview Calculus I: Problem 7 (1 point) Let I' +5 f(I) = x2 - 1 Find the indicated one-sided limits of f. NOTE: Remember that you use INF for co and -INF for -co. You should also sketch a graph of y = f(@), including vertical and horizontal asymptotes. lim f(x) = lim f(x) = lim f(x) = lim f(x) = I +1+ lim f(x) = lim f(x) =Chapter 6 Review: Problem 8 (1 point) Suppose that f is an even function and g is an odd function and both are integrable on the interval [-a, a]. Given that fo f(x)dx = 2 and f g(x)dx = 3. If possible, find the following integrals: 1. J.g(x)di = OA. 6 OB. The given information is not enough to find this integral OC. 4 OD. 0 2 f". f(x) . (g(z))2dr = OA. 324 OB. 6 OC. O OD. The given information is not enough to find this integral 1. . f(x)dx = OA. 0 OB. 4 O C. The given information is not enough to find this integral OD. 6 2. J .(5f(x) + 4g(x))di = OA. 20 OB. The given information is not enough to find this integral O C. 22 OD. 6 2 f(f(x))? . g(x)dx = OA. 16 OB. 0 OC. 48 OD. The given information is not enough to find this integralReview Calculus I. Problem of (1 point) A car is timed going down a track. Table 1 shows the distance the car is from the start line after it initially takes off. Table 2 shows the distance the car is from the finish line after it crosses the line and eventually comes to a stop. Table 1 Table 2 Time (s) Distance (ft) Time (s) Distance (ft) 0 0 0 0 2 18 2 552 4 41 4 902 6 121 6 1085 8 306 8 1164 10 585 10 1196 750 1450 350 11 Note: Click on any graph to view a larger graph. 1) From Table 1, calculate the average speed between t = 0 and t = 2: 2) From Table 1, calculate the average speed between t = 4 and t = 6: 3) From Table 1, calculate the average speed between t = 8 and t = 10: 4) From Table 2, calculate the average speed between t = 0 and t = 2: 5) From Table 2, calculate the average speed between t = 4 and t = 6: 6) From Table 2, calculate the average speed between t = 8 and t = 10:Chapter 6 Review: Problem 9 (1 point) You want to estimate the area underneath the graph of a positive function by using 4000 rectangles of equal width. The rectangles that must give the best estimate of this area are those with height obtained from the: D A. Midpoints D B. Right endpoints D C. Leit endpoints D D. We do not have enough information to decide. Review Calculus I: Problem 9 (1 point) Let f(x) = I' + 81. (A) Find the slope of the secant line joining (3, f(3)) and (7, f(7)). Slope of secant line = (B) Find the slope of the secant line joining (4, f(4) ) and (4 + h, f(4 + h)). Slope of secant line = (C) Find the slope of the tangent line at (4, f(4)). Slope of tangent line = (D) Find the equation of the tangent line at (4, f (4)). y