In Exercises 1–10, evaluate 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_forwardFor the functions in Exercises 39–42,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 Exercises 3–6, write a in the form a = aTT + aNN at the given value of t without finding T and N.arrow_forwardCalculate 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 Exercises 35–37, use Theorem 1 to derive the formula.arrow_forward
- In Exercises 21–26, evaluate det(A) by a cofactor expansion along a row or column of your choice.arrow_forwardSection 5.7 p. 613 # 398, 402 In the following exercises, find each indefinite integral, using appropriate substitutions. dx V1-16x 398. dx |x|/4x² -16 402.arrow_forwardShow that 4x2 + 6x + 3 is a unit in Z8[x].arrow_forward
- In Exercises 31–38, find the absolute maxima and minima of the func-tions on the given domains.arrow_forwardUse the addition formulas to derive the identities in Exercises 31–36.arrow_forwardIn Problems 31–34, find the complex zeros of each polynomial function f1x). Write f in factored form.arrow_forward
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