a. Explanation Given Information: A function f is an integrable on [ a , b ] and x k = a + k ( b − a ) n . Proof: The accumulation function of the area A ( x ) can be written using the definition of the definite integral to find the area under the curve between the function and the x − axis on the interval [ a , b ] as given below. The exact value of the area on the interval [ a , b ] A ( x ) = ∫ a b f ( x ) d x The average of the area on the interval [ a , b ] = 1 b − a ∫ a b f ( x ) d x The approximation for the sum of areas of small rectangles with width 1 n and height f ( x n ) where n = 1 , 2 , 3 , ..... , n on the interval [ a , b ] can be calculated as given below. A ( x ) = 1 n . f ( x 1 ) + 1 n b. To determine To Explain: the left hand sideof the equation is a calculationof average value algebraically c. To determine To explain: the right hand sideof the equation is a calculationof average value geometrically

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

See similar textbooks

Videos

Question

Chapter 4.6, Problem 81P

To determine

To Prove: limn→∞∑k=1nf(xk)n=1b−a∫abf(x)dx using the definition of definite integral as a limit of Riemann sums

To determine

To Explain: the left hand sideof the equation is a calculationof average value algebraically

To determine

To explain: the right hand sideof the equation is a calculationof average value geometrically

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.6, Problem 80P

Chapter 4.6, Problem 82P

Students have asked these similar questions

Q3. Determine the effective annual yield for each investment below. Then select the better investment. Assume 365 days in a year. a) 5.6% compounded semiannually; b) 5.4% compounded daily.

Q2. You deposit $22,000 in an account that pays 4.8% interest compounded monthly. a. Find the future value after six years. & b b. Determine the effective annual yield of this account.

18. Using the method of variation of parameter, a particular solution to y′′ + 16y = 4 sec(4t) isyp(t) = u1(t) cos(4t) + u2(t) sin(4t). Then u2(t) is equal toA. 1 B. t C. ln | sin 4t| D. ln | cos 4t| E. sec(4t)

Chapter 4 Solutions

Loose-leaf Version for Calculus

Ch. 4.1 - Prob. 1TB Ch. 4.1 - Prob. 2TB Ch. 4.1 - Prob. 3TB Ch. 4.1 - Prob. 0C Ch. 4.1 - Prob. 1C Ch. 4.1 - Prob. 2C Ch. 4.1 - Prob. 3C Ch. 4.1 - Prob. 4C Ch. 4.1 - Prob. 5C Ch. 4.1 - Prob. 6C

Ch. 4.1 - Prob. 7C Ch. 4.1 - Prob. 8C Ch. 4.1 - Prob. 9C Ch. 4.1 - Prob. 10C Ch. 4.1 - Prob. 11C Ch. 4.1 - Prob. 12C Ch. 4.1 - Prob. 13C Ch. 4.1 - Prob. 14C Ch. 4.1 - Prob. 15C Ch. 4.1 - Prob. 16C Ch. 4.1 - Prob. 17C Ch. 4.1 - Prob. 18C Ch. 4.1 - Prob. 19C Ch. 4.1 - Prob. 20C Ch. 4.1 - Prob. 21S Ch. 4.1 - Prob. 22S Ch. 4.1 - Prob. 23S Ch. 4.1 - Prob. 24S Ch. 4.1 - Prob. 25S Ch. 4.1 - Prob. 26S Ch. 4.1 - Prob. 27S Ch. 4.1 - Prob. 28S Ch. 4.1 - Prob. 29S Ch. 4.1 - Prob. 30S Ch. 4.1 - Prob. 31S Ch. 4.1 - Prob. 32S Ch. 4.1 - Prob. 33S Ch. 4.1 - Prob. 34S Ch. 4.1 - Prob. 35S Ch. 4.1 - Prob. 36S Ch. 4.1 - Prob. 37S Ch. 4.1 - Prob. 38S Ch. 4.1 - Prob. 39S Ch. 4.1 - Prob. 40S Ch. 4.1 - Prob. 41S Ch. 4.1 - Prob. 42S Ch. 4.1 - Prob. 43S Ch. 4.1 - Prob. 44S Ch. 4.1 - Prob. 45S Ch. 4.1 - Prob. 46S Ch. 4.1 - Prob. 47S Ch. 4.1 - Prob. 48S Ch. 4.1 - Prob. 49S Ch. 4.1 - Prob. 50S Ch. 4.1 - Prob. 51S Ch. 4.1 - Prob. 52S Ch. 4.1 - Prob. 53A Ch. 4.1 - Prob. 54A Ch. 4.1 - Prob. 55A Ch. 4.1 - Prob. 56A Ch. 4.1 - Prob. 57A Ch. 4.1 - Prob. 58P Ch. 4.1 - Prob. 59P Ch. 4.1 - Prob. 60P Ch. 4.1 - Prob. 61P Ch. 4.1 - Prob. 62P Ch. 4.1 - Prob. 1TF Ch. 4.1 - Prob. 2TF Ch. 4.1 - Prob. 3TF Ch. 4.1 - Prob. 4TF Ch. 4.1 - Prob. 5TF Ch. 4.1 - Prob. 6TF Ch. 4.1 - Prob. 7TF Ch. 4.2 - Prob. 1TB Ch. 4.2 - Prob. 0C Ch. 4.2 - Prob. 1C Ch. 4.2 - Prob. 2C Ch. 4.2 - Prob. 3C Ch. 4.2 - Prob. 4C Ch. 4.2 - Prob. 5C Ch. 4.2 - Prob. 6C Ch. 4.2 - Prob. 7C Ch. 4.2 - Prob. 8C Ch. 4.2 - Prob. 9C Ch. 4.2 - Prob. 10C Ch. 4.2 - Prob. 11C Ch. 4.2 - Prob. 12C Ch. 4.2 - Prob. 13C Ch. 4.2 - Prob. 14C Ch. 4.2 - Prob. 15C Ch. 4.2 - Prob. 16C Ch. 4.2 - Prob. 17C Ch. 4.2 - Prob. 18C Ch. 4.2 - Prob. 19C Ch. 4.2 - Prob. 20C Ch. 4.2 - Prob. 21S Ch. 4.2 - Prob. 22S Ch. 4.2 - Prob. 23S Ch. 4.2 - Prob. 24S Ch. 4.2 - Prob. 25S Ch. 4.2 - Prob. 26S Ch. 4.2 - Prob. 27S Ch. 4.2 - Prob. 28S Ch. 4.2 - Prob. 29S Ch. 4.2 - Prob. 30S Ch. 4.2 - Prob. 31S Ch. 4.2 - Prob. 32S Ch. 4.2 - Prob. 33S Ch. 4.2 - Prob. 34S Ch. 4.2 - Prob. 35S Ch. 4.2 - Prob. 36S Ch. 4.2 - Prob. 37S Ch. 4.2 - Prob. 38S Ch. 4.2 - Prob. 39S Ch. 4.2 - Prob. 40S Ch. 4.2 - Prob. 41S Ch. 4.2 - Prob. 42S Ch. 4.2 - Prob. 43S Ch. 4.2 - Prob. 44S Ch. 4.2 - Prob. 45A Ch. 4.2 - Prob. 46A Ch. 4.2 - Prob. 47A Ch. 4.2 - Prob. 48A Ch. 4.2 - Prob. 49A Ch. 4.2 - Prob. 50P Ch. 4.2 - Prob. 51P Ch. 4.2 - Prob. 52P Ch. 4.2 - Prob. 53P Ch. 4.2 - Prob. 1TF Ch. 4.2 - Prob. 2TF Ch. 4.2 - Prob. 3TF Ch. 4.2 - Prob. 4TF Ch. 4.2 - Prob. 5TF Ch. 4.2 - Prob. 6TF Ch. 4.2 - Prob. 7TF Ch. 4.2 - Prob. 8TF Ch. 4.2 - Prob. 9TF Ch. 4.2 - Prob. 10TF Ch. 4.2 - Prob. 11TF Ch. 4.3 - Prob. 1TB Ch. 4.3 - Prob. 2TB Ch. 4.3 - Prob. 0C Ch. 4.3 - Prob. 1C Ch. 4.3 - Prob. 2C Ch. 4.3 - Prob. 3C Ch. 4.3 - Prob. 4C Ch. 4.3 - Prob. 5C Ch. 4.3 - Prob. 6C Ch. 4.3 - Prob. 7C Ch. 4.3 - Prob. 8C Ch. 4.3 - Prob. 9C Ch. 4.3 - Prob. 10C Ch. 4.3 - Prob. 11C Ch. 4.3 - Prob. 12C Ch. 4.3 - Prob. 13C Ch. 4.3 - Prob. 14C Ch. 4.3 - Prob. 15C Ch. 4.3 - Prob. 16C Ch. 4.3 - Prob. 17C Ch. 4.3 - Prob. 18C Ch. 4.3 - Prob. 19C Ch. 4.3 - Prob. 20C Ch. 4.3 - Prob. 21S Ch. 4.3 - Prob. 22S Ch. 4.3 - Prob. 23S Ch. 4.3 - Prob. 24S Ch. 4.3 - Prob. 25S Ch. 4.3 - Prob. 26S Ch. 4.3 - Prob. 27S Ch. 4.3 - Prob. 28S Ch. 4.3 - Prob. 29S Ch. 4.3 - Prob. 30S Ch. 4.3 - Prob. 31S Ch. 4.3 - Prob. 32S Ch. 4.3 - Prob. 33S Ch. 4.3 - Prob. 34S Ch. 4.3 - Prob. 35S Ch. 4.3 - Prob. 36S Ch. 4.3 - Prob. 37S Ch. 4.3 - Prob. 38S Ch. 4.3 - Prob. 39S Ch. 4.3 - Prob. 40S Ch. 4.3 - Prob. 41S Ch. 4.3 - Prob. 42S Ch. 4.3 - Prob. 43S Ch. 4.3 - Prob. 44S Ch. 4.3 - Prob. 45S Ch. 4.3 - Prob. 46S Ch. 4.3 - Prob. 47S Ch. 4.3 - Prob. 48S Ch. 4.3 - Prob. 49S Ch. 4.3 - Prob. 50S Ch. 4.3 - Prob. 51S Ch. 4.3 - Prob. 52S Ch. 4.3 - Prob. 53A Ch. 4.3 - Prob. 54A Ch. 4.3 - Prob. 55P Ch. 4.3 - Prob. 56P Ch. 4.3 - Prob. 57P Ch. 4.3 - Prob. 58P Ch. 4.3 - Prob. 59P Ch. 4.3 - Prob. 60P Ch. 4.3 - Prob. 61P Ch. 4.3 - Prob. 62P Ch. 4.3 - Prob. 1TF Ch. 4.3 - Prob. 2TF Ch. 4.3 - Prob. 3TF Ch. 4.3 - Prob. 4TF Ch. 4.4 - Prob. 1TB Ch. 4.4 - Prob. 2TB Ch. 4.4 - Prob. 3TB Ch. 4.4 - Prob. 4TB Ch. 4.4 - Prob. 0C Ch. 4.4 - Prob. 1C Ch. 4.4 - Prob. 2C Ch. 4.4 - Prob. 3C Ch. 4.4 - Prob. 4C Ch. 4.4 - Prob. 5C Ch. 4.4 - Prob. 6C Ch. 4.4 - Prob. 7C Ch. 4.4 - Prob. 8C Ch. 4.4 - Prob. 9C Ch. 4.4 - Prob. 10C Ch. 4.4 - Prob. 11C Ch. 4.4 - Prob. 12C Ch. 4.4 - Prob. 13C Ch. 4.4 - Prob. 14C Ch. 4.4 - Prob. 15C Ch. 4.4 - Prob. 16C Ch. 4.4 - Prob. 17C Ch. 4.4 - Prob. 18C Ch. 4.4 - Prob. 19C Ch. 4.4 - Prob. 20C Ch. 4.4 - Prob. 21S Ch. 4.4 - Prob. 22S Ch. 4.4 - Prob. 23S Ch. 4.4 - Prob. 24S Ch. 4.4 - Prob. 25S Ch. 4.4 - Prob. 26S Ch. 4.4 - Prob. 27S Ch. 4.4 - Prob. 28S Ch. 4.4 - Prob. 29S Ch. 4.4 - Prob. 30S Ch. 4.4 - Prob. 31S Ch. 4.4 - Prob. 32S Ch. 4.4 - Prob. 33S Ch. 4.4 - Prob. 34S Ch. 4.4 - Prob. 35S Ch. 4.4 - Prob. 36S Ch. 4.4 - Prob. 37S Ch. 4.4 - Prob. 38S Ch. 4.4 - Prob. 39S Ch. 4.4 - Prob. 40S Ch. 4.4 - Prob. 41S Ch. 4.4 - Prob. 42S Ch. 4.4 - Prob. 43S Ch. 4.4 - Prob. 44S Ch. 4.4 - Prob. 45S Ch. 4.4 - Prob. 46S Ch. 4.4 - Prob. 47S Ch. 4.4 - Prob. 48S Ch. 4.4 - Prob. 49S Ch. 4.4 - Prob. 50S Ch. 4.4 - Prob. 51S Ch. 4.4 - Prob. 52S Ch. 4.4 - Prob. 53S Ch. 4.4 - Prob. 54S Ch. 4.4 - Prob. 55S Ch. 4.4 - Prob. 56S Ch. 4.4 - Prob. 57S Ch. 4.4 - Prob. 58S Ch. 4.4 - Prob. 59S Ch. 4.4 - Prob. 60S Ch. 4.4 - Prob. 61S Ch. 4.4 - Prob. 62S Ch. 4.4 - Prob. 63S Ch. 4.4 - Prob. 64S Ch. 4.4 - Prob. 65S Ch. 4.4 - Prob. 66S Ch. 4.4 - Prob. 67S Ch. 4.4 - Prob. 68S Ch. 4.4 - Prob. 69A Ch. 4.4 - Prob. 70A Ch. 4.4 - Prob. 71P Ch. 4.4 - Prob. 72P Ch. 4.4 - Prob. 73P Ch. 4.4 - Prob. 74P Ch. 4.4 - Prob. 75P Ch. 4.4 - Prob. 76P Ch. 4.4 - Prob. 77P Ch. 4.4 - Prob. 78P Ch. 4.4 - Prob. 79P Ch. 4.4 - Prob. 1TF Ch. 4.4 - Prob. 2TF Ch. 4.4 - Prob. 3TF Ch. 4.4 - Prob. 4TF Ch. 4.4 - Prob. 5TF Ch. 4.4 - Prob. 6TF Ch. 4.4 - Prob. 7TF Ch. 4.4 - Prob. 8TF Ch. 4.4 - Prob. 9TF Ch. 4.4 - Prob. 10TF Ch. 4.5 - Prob. 1TB Ch. 4.5 - Prob. 2TB Ch. 4.5 - Prob. 3TB Ch. 4.5 - Prob. 4TB Ch. 4.5 - Prob. 0C Ch. 4.5 - Prob. 1C Ch. 4.5 - Prob. 2C Ch. 4.5 - Prob. 3C Ch. 4.5 - Prob. 4C Ch. 4.5 - Prob. 5C Ch. 4.5 - Prob. 6C Ch. 4.5 - Prob. 7C Ch. 4.5 - Prob. 8C Ch. 4.5 - Prob. 9C Ch. 4.5 - Prob. 10C Ch. 4.5 - Prob. 11C Ch. 4.5 - Prob. 12C Ch. 4.5 - Prob. 13C Ch. 4.5 - Prob. 14C Ch. 4.5 - Prob. 15C Ch. 4.5 - Prob. 16C Ch. 4.5 - Prob. 17C Ch. 4.5 - Prob. 18C Ch. 4.5 - Prob. 19S Ch. 4.5 - Prob. 20S Ch. 4.5 - Prob. 21S Ch. 4.5 - Prob. 22S Ch. 4.5 - Prob. 23S Ch. 4.5 - Prob. 24S Ch. 4.5 - Prob. 25S Ch. 4.5 - Prob. 26S Ch. 4.5 - Prob. 27S Ch. 4.5 - Prob. 28S Ch. 4.5 - Prob. 29S Ch. 4.5 - Prob. 30S Ch. 4.5 - Prob. 31S Ch. 4.5 - Prob. 32S Ch. 4.5 - Prob. 33S Ch. 4.5 - Prob. 34S Ch. 4.5 - Prob. 35S Ch. 4.5 - Prob. 36S Ch. 4.5 - Prob. 37S Ch. 4.5 - Prob. 38S Ch. 4.5 - Prob. 39S Ch. 4.5 - Prob. 40S Ch. 4.5 - Prob. 41S Ch. 4.5 - Prob. 42S Ch. 4.5 - Prob. 43S Ch. 4.5 - Prob. 44S Ch. 4.5 - Prob. 45S Ch. 4.5 - Prob. 46S Ch. 4.5 - Prob. 47S Ch. 4.5 - Prob. 48S Ch. 4.5 - Prob. 49S Ch. 4.5 - Prob. 50S Ch. 4.5 - Prob. 51S Ch. 4.5 - Prob. 52S Ch. 4.5 - Prob. 53S Ch. 4.5 - Prob. 54S Ch. 4.5 - Prob. 55S Ch. 4.5 - Prob. 56S Ch. 4.5 - Prob. 57S Ch. 4.5 - Prob. 58S Ch. 4.5 - Prob. 59S Ch. 4.5 - Prob. 60S Ch. 4.5 - Prob. 61S Ch. 4.5 - Prob. 62S Ch. 4.5 - Prob. 63S Ch. 4.5 - Prob. 64S Ch. 4.5 - Prob. 65A Ch. 4.5 - Prob. 66A Ch. 4.5 - Prob. 67A Ch. 4.5 - Prob. 68A Ch. 4.5 - Prob. 69A Ch. 4.5 - Prob. 70A Ch. 4.5 - Prob. 71A Ch. 4.5 - Prob. 72P Ch. 4.5 - Prob. 73P Ch. 4.5 - Prob. 74P Ch. 4.5 - Prob. 75P Ch. 4.5 - Prob. 76P Ch. 4.5 - Prob. 77P Ch. 4.5 - Prob. 78P Ch. 4.5 - Prob. 79P Ch. 4.5 - Prob. 80P Ch. 4.5 - Prob. 1TF Ch. 4.5 - Prob. 2TF Ch. 4.5 - Prob. 3TF Ch. 4.5 - Prob. 4TF Ch. 4.5 - Prob. 5TF Ch. 4.5 - Prob. 6TF Ch. 4.6 - Prob. 1TB Ch. 4.6 - Prob. 2TB Ch. 4.6 - Prob. 3TB Ch. 4.6 - Prob. 4TB Ch. 4.6 - Prob. 5TB Ch. 4.6 - Prob. 0C Ch. 4.6 - Prob. 1C Ch. 4.6 - Prob. 2C Ch. 4.6 - Prob. 3C Ch. 4.6 - Prob. 4C Ch. 4.6 - Prob. 5C Ch. 4.6 - Prob. 6C Ch. 4.6 - Prob. 7C Ch. 4.6 - Prob. 8C Ch. 4.6 - Prob. 9C Ch. 4.6 - Prob. 10C Ch. 4.6 - Prob. 11C Ch. 4.6 - Prob. 12C Ch. 4.6 - Prob. 13C Ch. 4.6 - Prob. 14C Ch. 4.6 - Prob. 15C Ch. 4.6 - Prob. 16C Ch. 4.6 - Prob. 17C Ch. 4.6 - Prob. 18C Ch. 4.6 - Prob. 19C Ch. 4.6 - Prob. 20C Ch. 4.6 - Prob. 21C Ch. 4.6 - Prob. 22C Ch. 4.6 - Prob. 23S Ch. 4.6 - Prob. 24S Ch. 4.6 - Prob. 25S Ch. 4.6 - Prob. 26S Ch. 4.6 - Prob. 27S Ch. 4.6 - Prob. 28S Ch. 4.6 - Prob. 29S Ch. 4.6 - Prob. 30S Ch. 4.6 - Prob. 31S Ch. 4.6 - Prob. 32S Ch. 4.6 - Prob. 33S Ch. 4.6 - Prob. 34S Ch. 4.6 - Prob. 35S Ch. 4.6 - Prob. 36S Ch. 4.6 - Prob. 37S Ch. 4.6 - Prob. 38S Ch. 4.6 - Prob. 39S Ch. 4.6 - Prob. 40S Ch. 4.6 - Prob. 41S Ch. 4.6 - Prob. 42S Ch. 4.6 - Prob. 43S Ch. 4.6 - Prob. 44S Ch. 4.6 - Prob. 45S Ch. 4.6 - Prob. 46S Ch. 4.6 - Prob. 47S Ch. 4.6 - Prob. 48S Ch. 4.6 - Prob. 49S Ch. 4.6 - Prob. 50S Ch. 4.6 - Prob. 51S Ch. 4.6 - Prob. 52S Ch. 4.6 - Prob. 53S Ch. 4.6 - Prob. 54S Ch. 4.6 - Prob. 55S Ch. 4.6 - Prob. 56S Ch. 4.6 - Prob. 57S Ch. 4.6 - Prob. 58S Ch. 4.6 - Prob. 59S Ch. 4.6 - Prob. 60S Ch. 4.6 - Prob. 61S Ch. 4.6 - Prob. 62S Ch. 4.6 - Prob. 63S Ch. 4.6 - Prob. 64S Ch. 4.6 - Prob. 65S Ch. 4.6 - Prob. 66S Ch. 4.6 - Prob. 67S Ch. 4.6 - Prob. 68S Ch. 4.6 - Prob. 69S Ch. 4.6 - Prob. 70S Ch. 4.6 - Prob. 71S Ch. 4.6 - Prob. 72S Ch. 4.6 - Prob. 73S Ch. 4.6 - Prob. 74A Ch. 4.6 - Prob. 75A Ch. 4.6 - Prob. 76A Ch. 4.6 - Prob. 77A Ch. 4.6 - Prob. 78P Ch. 4.6 - Prob. 79P Ch. 4.6 - Prob. 80P Ch. 4.6 - Prob. 81P Ch. 4.6 - Prob. 82P Ch. 4.6 - Prob. 1TF Ch. 4.6 - Prob. 2TF Ch. 4.6 - Prob. 3TF Ch. 4.6 - Prob. 4TF Ch. 4.6 - Prob. 5TF Ch. 4.7 - Prob. 1TB Ch. 4.7 - Prob. 2TB Ch. 4.7 - Prob. 3TB Ch. 4.7 - Prob. 0C Ch. 4.7 - Prob. 1C Ch. 4.7 - Prob. 2C Ch. 4.7 - Prob. 3C Ch. 4.7 - Prob. 4C Ch. 4.7 - Prob. 5C Ch. 4.7 - Prob. 6C Ch. 4.7 - Prob. 7C Ch. 4.7 - Prob. 8C Ch. 4.7 - Prob. 9C Ch. 4.7 - Prob. 10C Ch. 4.7 - Prob. 11C Ch. 4.7 - Prob. 12C Ch. 4.7 - Prob. 13C Ch. 4.7 - Prob. 14C Ch. 4.7 - Prob. 15C Ch. 4.7 - Prob. 16C Ch. 4.7 - Prob. 17C Ch. 4.7 - Prob. 18C Ch. 4.7 - Prob. 19C Ch. 4.7 - Prob. 20C Ch. 4.7 - Prob. 21C Ch. 4.7 - Prob. 22C Ch. 4.7 - Prob. 23C Ch. 4.7 - Prob. 24C Ch. 4.7 - Prob. 25C Ch. 4.7 - Prob. 26C Ch. 4.7 - Prob. 27S Ch. 4.7 - Prob. 28S Ch. 4.7 - Prob. 29S Ch. 4.7 - Prob. 30S Ch. 4.7 - Prob. 31S Ch. 4.7 - Prob. 32S Ch. 4.7 - Prob. 33S Ch. 4.7 - Prob. 34S Ch. 4.7 - Prob. 35S Ch. 4.7 - Prob. 36S Ch. 4.7 - Prob. 37S Ch. 4.7 - Prob. 38S Ch. 4.7 - Prob. 39S Ch. 4.7 - Prob. 40S Ch. 4.7 - Prob. 41S Ch. 4.7 - Prob. 42S Ch. 4.7 - Prob. 43S Ch. 4.7 - Prob. 44S Ch. 4.7 - Prob. 45S Ch. 4.7 - Prob. 46S Ch. 4.7 - Prob. 47S Ch. 4.7 - Prob. 48S Ch. 4.7 - Prob. 49S Ch. 4.7 - Prob. 50S Ch. 4.7 - Prob. 51S Ch. 4.7 - Prob. 52S Ch. 4.7 - Prob. 53S Ch. 4.7 - Prob. 54S Ch. 4.7 - Prob. 55S Ch. 4.7 - Prob. 56S Ch. 4.7 - Prob. 57S Ch. 4.7 - Prob. 58S Ch. 4.7 - Prob. 59A Ch. 4.7 - Prob. 60A Ch. 4.7 - Prob. 61A Ch. 4.7 - Prob. 62A Ch. 4.7 - Prob. 63P Ch. 4.7 - Prob. 64P Ch. 4.7 - Prob. 65P Ch. 4.7 - Prob. 66P Ch. 4.7 - Prob. 67P Ch. 4.7 - Prob. 68P Ch. 4.7 - Prob. 69P Ch. 4.7 - Prob. 70P Ch. 4.7 - Prob. 71P Ch. 4.7 - Prob. 72P Ch. 4.7 - Prob. 73P Ch. 4.7 - Prob. 74P Ch. 4.7 - Prob. 75P Ch. 4.7 - Prob. 76P Ch. 4.7 - Prob. 77P Ch. 4.7 - Prob. 78P Ch. 4.7 - Prob. 1TF Ch. 4.7 - Prob. 2TF Ch. 4.7 - Prob. 3TF Ch. 4.7 - Prob. 4TF Ch. 4.7 - Prob. 5TF Ch. 4.7 - Prob. 6TF Ch. 4.7 - Prob. 7TF Ch. 4.7 - Prob. 8TF Ch. 4 - Prob. 1D Ch. 4 - Prob. 2D Ch. 4 - Prob. 3D Ch. 4 - Prob. 4D Ch. 4 - Prob. 5D Ch. 4 - Prob. 6D Ch. 4 - Prob. 7D Ch. 4 - Prob. 8D Ch. 4 - Prob. 9D Ch. 4 - Prob. 10D Ch. 4 - Prob. 11D Ch. 4 - Prob. 12D Ch. 4 - Prob. 13D Ch. 4 - Prob. 1T Ch. 4 - Prob. 2T Ch. 4 - Prob. 3T Ch. 4 - Prob. 4T Ch. 4 - Prob. 5T Ch. 4 - Prob. 6T Ch. 4 - Prob. 7T Ch. 4 - Prob. 8T Ch. 4 - Prob. 9T Ch. 4 - Prob. 10T Ch. 4 - Prob. 11T Ch. 4 - Prob. 12T Ch. 4 - Prob. 13T Ch. 4 - Prob. 1NFAR Ch. 4 - Prob. 2NFAR Ch. 4 - Prob. 3NFAR Ch. 4 - Prob. 4NFAR Ch. 4 - Prob. 5NFAR Ch. 4 - Prob. 6NFAR Ch. 4 - Prob. 7NFAR Ch. 4 - Prob. 8NFAR Ch. 4 - Prob. 9NFAR Ch. 4 - Prob. 10NFAR Ch. 4 - Prob. 11NFAR Ch. 4 - Prob. 12NFAR Ch. 4 - Prob. 13NFAR Ch. 4 - Prob. 14NFAR Ch. 4 - Prob. 15NFAR Ch. 4 - Prob. 16NFAR Ch. 4 - Prob. 17NFAR Ch. 4 - Prob. 18NFAR Ch. 4 - Prob. 19NFAR Ch. 4 - Prob. 20NFAR Ch. 4 - Prob. 21NFAR Ch. 4 - Prob. 22NFAR Ch. 4 - Prob. 23NFAR Ch. 4 - Prob. 24NFAR Ch. 4 - Prob. 25NFAR Ch. 4 - Prob. 26NFAR Ch. 4 - Prob. 27NFAR Ch. 4 - Prob. 28NFAR Ch. 4 - Prob. 29NFAR Ch. 4 - Prob. 30NFAR Ch. 4 - Prob. 31NFAR Ch. 4 - Prob. 32NFAR Ch. 4 - Prob. 33NFAR Ch. 4 - Prob. 34NFAR Ch. 4 - Prob. 35NFAR Ch. 4 - Prob. 36NFAR Ch. 4 - Prob. 37NFAR Ch. 4 - Prob. 38NFAR Ch. 4 - Prob. 39NFAR Ch. 4 - Prob. 40NFAR Ch. 4 - Prob. 41NFAR Ch. 4 - Prob. 42NFAR Ch. 4 - Prob. 43NFAR Ch. 4 - Prob. 44NFAR Ch. 4 - Prob. 45NFAR Ch. 4 - Prob. 46NFAR Ch. 4 - Prob. 47NFAR Ch. 4 - Prob. 48NFAR Ch. 4 - Prob. 49NFAR Ch. 4 - Prob. 50NFAR Ch. 4 - Prob. 51NFAR Ch. 4 - Prob. 52NFAR Ch. 4 - Prob. 53NFAR Ch. 4 - Prob. 54NFAR Ch. 4 - Prob. 1SC Ch. 4 - Prob. 2SC Ch. 4 - Prob. 3SC Ch. 4 - Prob. 4SC Ch. 4 - Prob. 5SC Ch. 4 - Prob. 6SC Ch. 4 - Prob. 7SC Ch. 4 - Prob. 8SC Ch. 4 - Prob. 9SC Ch. 4 - Prob. 10SC Ch. 4 - Prob. 11SC Ch. 4 - Prob. 12SC Ch. 4 - Prob. 13SC Ch. 4 - Prob. 14SC Ch. 4 - Prob. 15SC Ch. 4 - Prob. 16SC Ch. 4 - Prob. 17SC Ch. 4 - Prob. 18SC Ch. 4 - Prob. 19SC Ch. 4 - Prob. 20SC Ch. 4 - Prob. 21SC Ch. 4 - Prob. 22SC Ch. 4 - Prob. 23SC Ch. 4 - Prob. 24SC Ch. 4 - Prob. 25SC Ch. 4 - Prob. 26SC Ch. 4 - Prob. 27SC Ch. 4 - Prob. 28SC Ch. 4 - Prob. 29SC Ch. 4 - Prob. 30SC Ch. 4 - Prob. 31SC Ch. 4 - Prob. 32SC Ch. 4 - Prob. 33SC Ch. 4 - Prob. 34SC Ch. 4 - Prob. 35SC Ch. 4 - Prob. 36SC Ch. 4 - Prob. 37SC Ch. 4 - Prob. 38SC Ch. 4 - Prob. 39SC Ch. 4 - Prob. 40SC Ch. 4 - Prob. 41SC Ch. 4 - Prob. 42SC Ch. 4 - Prob. 43SC Ch. 4 - Prob. 44SC Ch. 4 - Prob. 45SC Ch. 4 - Prob. 46SC Ch. 4 - Prob. ACP Ch. 4 - Prob. BCP Ch. 4 - Prob. CCP Ch. 4 - Prob. DCP

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To Prove: lim n → ∞ ∑ k = 1 n f ( x k ) n = 1 b − a ∫ a b f ( x ) d x using the definition of definite integral as a limit of Riemann sums

Solution Summary: The author explains how the accumulation function of the area A(x) can be written using the definition of definite integral.

Videos

To Prove: limn→∞∑k=1nf(xk)n=1b−a∫abf(x)dx using the definition of definite integral as a limit of Riemann sums

To Explain: the left hand sideof the equation is a calculationof average value algebraically

To explain: the right hand sideof the equation is a calculationof average value geometrically

Want to see the full answer?

Chapter 4 Solutions