By Ron Larson
CALCULUS I WITH PRECALCULUS, brings you up to the mark algebraically inside of precalculus and transition into calculus. The Larson Calculus application has been largely praised through a new release of scholars and professors for its strong and powerful pedagogy that addresses the wishes of a wide variety of training and studying types and environments. each one identify is only one part in a complete calculus direction software that rigorously integrates and coordinates print, media, and know-how items for winning educating and studying. One fundamental target guided the authors in penning this publication: to enhance special, readable fabrics for college students that truly outline and show techniques and principles of calculus.
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Extra resources for Calculus I with Precalculus, A One-Year Course, 3rd Edition
Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 1 Solving Equations 5 Quadratic Equations A quadratic equation in x is an equation that can be written in the general form ax2 ϩ bx ϩ c ϭ 0 where a, b, and c are real numbers, with a 0. A quadratic equation in x is also known as a second-degree polynomial equation in x. You should be familiar with the following four methods of solving quadratic equations. SOLVING A QUADRATIC EQUATION NOTE The Zero-Factor Property states that if the product of two factors is zero, then one (or both) of the factors must be zero.
X 2 Ϫ 3x x xϪ3 ͑x ϩ 2͒2 ϩ 5 ϭ ͑x ϩ 3͒2 ͑2x ϩ 1͒2 ϭ 4͑x 2 ϩ x ϩ 1͒ 15 6 Ϫ4ϭ ϩ3 x x 1 2 ϩ ϭ0 x xϪ5 7 8x Ϫ ϭ Ϫ4 2x ϩ 1 2x Ϫ 1 6 2 3͑x ϩ 5͒ Ϫ ϭ 2 x xϩ3 x ϩ 3x In Exercises 39– 42, write the quadratic equation in general form. 39. 2x 2 ϭ 3 Ϫ 8x 41. 15͑3x 2 Ϫ 10͒ ϭ 18x 40. 13 Ϫ 3͑x ϩ 7͒2 ϭ 0 42. x͑x ϩ 2͒ ϭ 5x 2 ϩ 1 In Exercises 43–54, solve the quadratic equation by factoring. 43. 45. 47. 49. 51. 53. 54. 44. 9x 2 Ϫ 4 ϭ 0 6x 2 ϩ 3x ϭ 0 46. x 2 Ϫ 10x ϩ 9 ϭ 0 x 2 Ϫ 2x Ϫ 8 ϭ 0 48. 4x 2 ϩ 12x ϩ 9 ϭ 0 x2 Ϫ 12x ϩ 35 ϭ 0 50.
Com for worked-out solutions to odd-numbered exercises. (h) In Exercises 1–6, fill in the blanks. 1. The set of all real numbers that are solutions of an inequality is the ________ ________ of the inequality. 2. The set of all points on the real number line that represents the solution set of an inequality is the ________ of the inequality. 3. To solve a linear inequality in one variable, you can use the properties of inequalities, which are identical to those used to solve equations, with the exception of multiplying or dividing each side by a ________ number.