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mathematics
calculus 10th edition

Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions

In Exercises, find the indefinite integral. x + 4 (x² + 8x - 7)² dx
In Exercises, find the indefinite integral. x(1 - 3x²)4 dx
In Exercises, find the indefinite integral. sin³ x cos x dx
In Exercises, find the indefinite integral. x² x³ + 3 dx
In Exercises, find the indefinite integral. fox³ 6x³ 3x4+2 dx
In Exercises, use the Second Fundamental Theorem of Calculus to find F'(x). F(x) = So csc² t dt
In Exercises, find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) -| 1 √x' [4,9]
In Exercises, use the Second Fundamental Theorem of Calculus to find F'(x). F(x) = [₁₂6² + -3 (t² + 3t+2) dt
In Exercises, use the Second Fundamental Theorem of Calculus to find F'(x). F(x) 1 S₁² = dt
In Exercises, use the Second Fundamental Theorem of Calculus to find F'(x). = SBVT+ Jo F(x) = 1²√ √1 + 1³ dt
In Exercises, find the area of the region bounded by the graphs of the equations. y = x - x³, x = 0, x = 1, y = 0
In Exercises, find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = x³, [0, 2]
In Exercises, find the area of the region bounded by the graphs of the equations. 0 = A*(x - 1) x^ = (
In Exercises, determine the area of the given region. y = x + cos x y RIN 3 2 RIN R 37
In Exercises, determine the area of the given region. y = sin x y -1 1 2 3 4 X
In Exercises, find the area of the region bounded by the graphs of the equations. y = -x² + x + 6, y = 0
In Exercises, use the Fundamental Theorem of Calculus to evaluate the definite integral. TT/4 J-π/4 sec² t dt
In Exercises, find the area of the region bounded by the graphs of the equations. y = 8 - x, x = 0, x = 6, y = 0
In Exercises, use the Fundamental Theorem of Calculus to evaluate the definite integral. x√x dx
In Exercises, use the Fundamental Theorem of Calculus to evaluate the definite integral. 2 (x4 + 4x 6) dx
In Exercises, use the Fundamental Theorem of Calculus to evaluate the definite integral. •3/4 0 sin Ꮎ dᎾ
In Exercises, use the Fundamental Theorem of Calculus to evaluate the definite integral. L -1 (41³ - 2t) dt
In Exercises, use the Fundamental Theorem of Calculus to evaluate the definite integral. fe- (t²-1)dt
In Exercises, use the Fundamental Theorem of Calculus to evaluate the definite integral. S x3 + x) dx
In Exercises, use the Fundamental Theorem of Calculus to evaluate the definite integral. *8 So 10 (3 + x) dx
In Exercises, sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral. f (5 - x - 5) dx
In Exercises, sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral.evaluate(a)(b)(c)(d) 3 fre f(x) dx = 4 and fr f(x) dx = -1
In Exercises, sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral.Givenevaluate(a)(b)(c)(d) 8 f(x) dx = 12 and (8 g(x) dx = 5
In Exercises, sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral. S. -6 36 - x² dx
In Exercises, set up a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) = 100 - x² y -15 60 40 20 15 -5 + 5 15 X
In Exercises, set up a definite integral that yields the area of the region. f(x) = 2x + 8 y -6 -2 00 8 4 2 -=2+ 2 4 X
In Exercises, use the limit process to find the area of the region bounded by the graph of the function and the -axis over the given interval. Sketch the region. y = x³, [2, 4]
Use the limit process to find the area of the region bounded by x = 5y - y², x = 0, y = 2, and y = 5.
In Exercises, use the properties of summation and Theorem 4.2 to evaluate the sum.Data from in Theorem 4.2 THEOREM 4.2 Summation Formulas 1. c = cn, c is a constant n(n + 1)(2n + 1) 6 n 3. Στ 2. 4. n n = n(n + 1) 2 = n²(n + 1)² 4 A proof of this theorem is given in Appendix
In Exercises, use the limit process to find the area of the region bounded by the graph of the function and the -axis over the given interval. Sketch the region. y = 5x², [-2, 1]
In Exercises, use the limit process to find the area of the region bounded by the graph of the function and the -axis over the given interval. Sketch the region. y = x² + 3, [0, 2]
In Exercises, use the properties of summation and Theorem 4.2 to evaluate the sum.Data from in Theorem 4.2 THEOREM 4.2 Summation Formulas 1. c = cn, c is a constant n(n + 1)(2n + 1) 6 n 3. Στ 2. 4. n n = n(n + 1) 2 = n²(n + 1)² 4 A proof of this theorem is given in Appendix A. See
In Exercises, use the limit process to find the area of the region bounded by the graph of the function and the -axis over the given interval. Sketch the region. y = 8 - 2x, [0, 3] =
In Exercises, use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width.) 1 y = 9-7x² 10 8 6 4 2 y 2 4 X
In Exercises, use the properties of summation and Theorem 4.2 to evaluate the sum.Data from in Theorem 4.2 THEOREM 4.2 Summation Formulas 1. c = cn, c is a constant n(n + 1)(2n + 1) 6 n 3. Στ 2. 4. n n = n(n + 1) 2 = n²(n + 1)² 4 A proof of this theorem is given in Appendix A. See
In Exercises, use sigma notation to write the sum. 3 1 (²-) ( ¹ + ¹)² + (²-) (² + ¹)²³ + n n n + 3 n+ (-)(^*')² n n 2
In Exercises, use the properties of summation and Theorem 4.2 to evaluate the sum.Data from in Theorem 4.2 THEOREM 4.2 Summation Formulas 1. c = cn, c is a constant n(n + 1)(2n + 1) 6 n 3. Στ 2. 4. n n = n(n + 1) 2 = n²(n + 1)² 4 A proof of this theorem is given in Appendix A. See
In Exercises, use the properties of summation and Theorem 4.2 to evaluate the sum.Data from in Theorem 4.2 THEOREM 4.2 Summation Formulas 1. c = cn, c is a constant n(n + 1)(2n + 1) 6 n 3. Στ 2. 4. n n = n(n + 1) 2 = n²(n + 1)² 4 A proof of this theorem is given in Appendix A. See
In Exercises, use sigma notation to write the sum. 1 + 3(1) 1 3(2) + 1 3(3) + + 1 3(10)
In Exercises, find the sum. Use the summation capabilities of a graphing utility to verify your result. 3 Σ (x2 + 1) 5 k=0 k = 0
In Exercises, find the sum. Use the summation capabilities of a graphing utility to verify your result. Σ(5i - 3) i=1
In Exercises a differential equation, a point, and a slope field are given. (a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the indicated point. (b) Use integration to find the particular solution of the differential
The table shows the velocities (in miles per hour) of two cars on an entrance ramp to an interstate highway. The time t is in seconds.(a) Rewrite the velocities in feet per second.(b) Use the regression capabilities of a graphing utility to find quadratic models for the data in part (a).(c)
In Exercises a differential equation, a point, and a slope field are given. (a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the indicated point. (b) Use integration to find the particular solution of the differential
In Exercises, find the particular solution that satisfies the differential equation and the initial condition. f"(x) = 2 cos x, f'(0) = 4, f(0) = -5
In Exercises, find the particular solution that satisfies the differential equation and the initial condition. f'(x) = -6x, f(1) = -2
In Exercises, find the particular solution that satisfies the differential equation and the initial condition. f"(x) = 24x, f'(-1) = 7, f(1) = −4
An airplane taking off from a runway travels 3600 feet before lifting off. The airplane starts from rest, moves with constant acceleration, and makes the run in 30 seconds. With what speed does it lift off?
In Exercises, find the particular solution that satisfies the differential equation and the initial condition. f'(x) = 9x² + 1, f(0) = 7
The speed of a car traveling in a straight line is reduced from 45 to 30 miles per hour in a distance of 264 feet. Find the distance in which the car can be brought to rest from 30 miles per hour, assuming the same constant deceleration.
In Exercises, find the indefinite integral. S (5 cos x 2 sec² x) dx
In Exercises, find the indefinite integral. 6 3/5 X dx
In Exercises, find the indefinite integral. Jo (2x - 9 sin x) dx
In Exercises, find the indefinite integral. x² + 2x - 6 x4
In Exercises, find the indefinite integral. J (4x² + x + 3) dx
In Exercises, find the indefinite integral. 8+ x3 dx
In Exercises, find the indefinite integral. fax++ (x+ + 3) dx
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. 2 4 + 1) dx, dx, n = 4
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. [²x³ dx Jo x³ dx, n = 4
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. S²² x² dx, n = 4
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. [²2/1/2dx dx, n = 4
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. J4 √x dx, n = 8
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. So 1 x³ dx, n = 6
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. So 3√x dx, n = 8
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. So 2 (x + 2)2 dx, n = 4
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. [x√x+14 x√x² + 1 dx, n = 4
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. 4 S (4x²) dx, n = 6
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. Jo √1 + x³ dx
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. 1 Jo 1 + x³ dx
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. So √x √1 - x dx
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. TT TT/2 √x sin x dx
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. 3.1 J3 cos x² dx
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. Jo TT/2 sin x² dx
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. TT/4 tan x² dx
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. TT ["* f(x) dx, f(x) = sin x X 1, x > 0 x = 0
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. TT/2 0 √1+ sin²x dx
In Exercises approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. π/4 0 x tan x dx
In Exercises use the error formulas in Theorem 4.20 to estimate the errors in approximating the integral, with n = 4, using (a) The Trapezoidal Rule(b) Simpson's Rule.Data from in Theorem 4.20 THEOREM 4.20 Errors in the Trapezoidal Rule and Simpson's Rule If f has a continuous second
In Exercises use the error formulas in Theorem 4.20 to estimate the errors in approximating the integral, with n = 4, using (a) The Trapezoidal Rule(b) Simpson's Rule.Data from in Theorem 4.20 THEOREM 4.20 Errors in the Trapezoidal Rule and Simpson's Rule If f has a continuous second
In Exercises use the error formulas in Theorem 4.20 to estimate the errors in approximating the integral, with n = 4, using (a) The Trapezoidal Rule(b) Simpson's Rule.Data from in Theorem 4.20 THEOREM 4.20 Errors in the Trapezoidal Rule and Simpson's Rule If f has a continuous second
The Trapezoidal Rule and Simpson's Rule yield approximations of a definite integral ∫ab ƒ(x) dx based on polynomial approximations of ƒ. What is the degree of the polynomials used for each?
Describe the size of the error when the Trapezoidal Rule is used to approximate ∫ab ƒ(x) dx when ƒ(x) is a linear function. Use a graph to explain your answer.
In Exercises use the error formulas in Theorem 4.20 to estimate the errors in approximating the integral, with n = 4, using (a) The Trapezoidal Rule(b) Simpson's Rule.Data from in Theorem 4.20 THEOREM 4.20 Errors in the Trapezoidal Rule and Simpson's Rule If f has a continuous second
In Exercises, solve the differential equation. dy dx 4x + 4x 16x²
In Exercises use the error formulas in Theorem 4.20 to find n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using (a) The Trapezoidal Rule (b) Simpson's Rule.Data from in Theorem 4.20 JI - dx X
In Exercises use the error formulas in Theorem 4.20 to find n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using (a) The Trapezoidal Rule (b) Simpson's Rule.Data from in Theorem 4.20 √x + 2 dx
In exercises, solve the differential equation. dy dx 10x² √1 + x³
In Exercises use the error formulas in Theorem 4.20 to find n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using (a) The Trapezoidal Rule (b) Simpson's Rule.Data from in Theorem 4.20 So i 1 1 + x dx
In Exercises use the error formulas in Theorem 4.20 to find n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using (a) The Trapezoidal Rule (b) Simpson's Rule.Data from in Theorem 4.20 *TT/2 0 sin x dx
In exercises, solve the differential equation. dy dx || x - 4 x² - 8x + 1
In Exercises use a computer algebra system and the error formulas to find n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using (a) TheTrapezoidal Rule (b) Simpson's Rule. So √1 + x dx
In Exercises use a computer algebra system and the error formulas to find n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using (a) The Trapezoidal Rule (b) Simpson's Rule. fax (x + 1)2/3 dx
In Exercises a differential equation, a point, and a slope field are given. A slop field consists of line segments with slopes given by the differential equation. These line segments give a visual perspective of the directions of the solutions of the differential equation. (a) Sketch two
In Exercises a differential equation, a point, and a slope field are given. A slop field consists of line segments with slopes given by the differential equation. These line segments give a visual perspective of the directions of the solutions of the differential equation. (a) Sketch two
In Exercises use a computer algebra system and the error formulas to find n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using (a) The Trapezoidal Rule (b) Simpson's Rule. So 0 tan x² dx

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