In Exercises 27–34, use technology to approximate the given
.Then decide whether the associated improper integral converges, and estimate its value to four significant digits if it does. [HINT: See the technology note for Example 1.]
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Applied Calculus
- In Exercises 1–14, to establish a big-O relationship, find wit- nesses C and k such that [f(x) k. 1. Determine whether each of these functions is O(x). a) f(x) = 10 c) f(x) = x² +x+ 1 e) f(x) = [x] b) f(x) — Зх +7 d) f(x) = 5 log x f) f(x) = [x/2] %3D %3Darrow_forwardSection 3.7 p. 343/345 # 350 Evaluate the following integrals. If the integral is not convergent, answer “divergent." 99 1 dx 1 xln x 350arrow_forwardIn Exercises 79–84, use the Comparison Test to determine whether the improper integral converges or diverges. dx 80. | (sin? x)e¬* dx 79. x² – 4arrow_forward
- Section 6: Compute the following indefinite integrals. (2) (10³ -2e³* )dxarrow_forwardSECTION 7.7 Approximate Integration 565 30. The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as indicated in the figure. Use Simpson's Rule to estimate the area of the pool. ra 5.6 5.0 6.8 4.8 4.8 7.2 6.2 31. (a) Use the Midpoint Rule and the given data to estimate the value of the integral f(x) dx. f(x) f(x) 1.0 24arrow_forwardShow that 1 cosec²(2) = > (z – nn)²" 2 -arrow_forward
- This is exercise 6 of Section 7.5 page 460. Find the integral tan(Va) dx | +Carrow_forwardSection 2.4 p. 180/182 # 172 For the following exercises, find the lengths of the functions of X over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. 2/3 y=x?3 from (1, 1) to (8, 4) 172arrow_forwardLet f(n) = 100(2" ) and g(n) = n!. Prove that f = O(g). %3Darrow_forward
- Show that if E,=1 a, diverges, then En=1 | |a,| diverges. %3Darrow_forwardLet X be the number of times a fair die is rolled until one appears twice in a row. Find E(X).arrow_forwardChapter 5, Section 5.5, Question 017 In each part, evaluate the integral, given that S lx – 18|,x > 0 f (x) = x+ 18, x < 0 (a) f(x)dx = (b) | f(x) dx = -18 (c) f (x) dx = (d) c22 f (x) dx = -20arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage