In Exercises 77–84, use Mike’s shortcut method (see Mike’s Shortcut Rule and the examples that follow) to calculate the given
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Applied Calculus
- In Exercises 45–50, use Taylor’s Theorem to obtain an upper bound for the error of the approximation. Then calculate the exact value of the errorarrow_forwardIn Exercises 39–44, each function f(x) changes value when x changes from x, to xo + dx. Find a. the change Af = f(xo + dx) – f(xo); b. the value of the estimate df = f'(xo) dx; and c. the approximation error |Af – df|. y = f(x)/ Af = f(xo + dx) – f(x) df = f'(xo) dx (xo, F(xo)) dx Tangent 0| xo + dx 39. f(x) 3D х? + 2x, хо —D 1, 40. f(x) = 2x² + 4x – 3, xo = -1, dx = 0.1 41. f(x) = x³ - x, xo = 1, dx = 0.1 dx = 0.1 %3D 42. f(x) 3 х, Хо —D 1, dx %3D 0.1 43. f(x) — х 1, Хо —D 0.5, dx %3D0.1 44. f(x) 3D х3 — 2х + 3, Хо — 2, dx 3D 0.1arrow_forwardIn Exercises 35–37, use Theorem 1 to derive the formula.arrow_forward
- Calculate z6 where z = 1 – 2j. [Hint: Pascal's triangle.] Calculate z10 where z = √3-j. [Hint: Use the exponential form and De Moivre's theorem.]arrow_forwardIn Problems 69–74, find the real zeros of f. If necessary, round to two decimal places.arrow_forwardFor Exercises 54–60, a. List all possible rational roots or rational zeros. b. Use Descartes's Rule of Signs to determine the possible number of positive and negative real roots or real zeros. c. Use synthetic division to test the possible rational roots or zeros and find an actual root or zero. d. Use the quotient from part (c) to find all the remaining roots or zeros. 54. f(x) = x' + 3x² – 4 55. flx) = 6x + x² – 4x + 1 %3D 56. 8x - 36xr? + 46x - 15 = 0 57. 2x + 9x2 - 7x + 1 = 0 58. x* - x - 7x2 + x + 6 = 0 59. 4x* + 7x - 2 = 0 60. f(x) = 2x* + x³ – 9x² – 4x + 4arrow_forward
- In Problems 37–42, analyze each rational functionarrow_forwardEach of Exercises 19–24 gives a formula for a function y = f(x). In each case, find f(x) and identify the domain and range of f¯1. 20. f(x) = x*, x > 0 22. f(x) = (1/2)x – 7/2 24. f(x) = 1/x³, x + 0 19. f(x) = x³ 21. f(x) = x³ + 1 23. f(x) = 1/x², x> 0 %3Darrow_forwardIn Exercises 13-14, find the domain of each function. 13. f(x) 3 (х +2)(х — 2) 14. g(x) (х + 2)(х — 2) In Exercises 15–22, let f(x) = x? – 3x + 8 and g(x) = -2x – 5.arrow_forward
- In Exercises 7–10,find the two x-intercepts of the function f andshow that f '(x) = 0 at some point between the twox-intercepts. f (x) = x2 − x − 2arrow_forwardIn Exercises 16–22, show that the two functions are inverses of each other. 2 16. f(x) = 3x + 2 and g(x) = 3arrow_forwardEvaluate the integrals in Exercises 5–8arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage