By Ron Larson
CALCULUS I WITH PRECALCULUS, brings you on top of things algebraically inside of precalculus and transition into calculus. The Larson Calculus software has been broadly praised via a iteration of scholars and professors for its reliable and powerful pedagogy that addresses the desires of a vast diversity of training and studying types and environments. each one identify is only one part in a complete calculus path software that rigorously integrates and coordinates print, media, and expertise items for winning instructing and studying. One fundamental aim guided the authors in scripting this e-book: to enhance unique, readable fabrics for college kids that sincerely outline and display suggestions and ideas of calculus
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Extra info for Calculus I with precalculus : a one-year course
X2 ϩ 3x ϩ 8 > 0 In Exercises 125–130, solve the inequality and write the solution set in interval notation. 125. 4x 3 Ϫ 6x 2 < 0 127. x3 Ϫ 4x Ն 0 129. ͑x Ϫ 1͒2͑x ϩ 2͒3 Ն 0 126. 4x 3 Ϫ 12x 2 > 0 128. 2x 3 Ϫ x 4 Յ 0 130. x 4͑x Ϫ 3͒ Յ 0 In Exercises 131–144, solve the inequality and graph the solution on the real number line. 131. 133. 135. 137. 139. 141. 143. 4x Ϫ 1 > 0 x 3x Ϫ 5 Ն0 xϪ5 xϩ6 Ϫ2 < 0 xϩ1 2 1 > xϩ5 xϪ3 1 9 Յ xϪ3 4x ϩ 3 x2 ϩ 2x Յ0 x2 Ϫ 9 3 2x ϩ > Ϫ1 xϪ1 xϩ1 132. 134. 136. 138. 140. 142.
B) Determine the minimum depth of the beam that will safely support a load of 2000 pounds. True or False? In Exercises 177–179, determine whether the statement is true or false. Justify your answer. 177. If a, b, and c are real numbers, and a Յ b, then ac Յ bc. 178. If Ϫ10 Յ x Յ 8, then Ϫ10 Ն Ϫx and Ϫx Ն Ϫ8. 3 179. The solution set of the inequality 2x 2 ϩ 3x ϩ 6 Ն 0 is the entire set of real numbers. CAPSTONE 180. Describe any differences between properties of equalities and properties of inequalities.
Unbounded intervals are of the form ͑Ϫ ϱ, b͒, ͑Ϫ ϱ, b͔, ͑a, ϱ͒, ͓a, ϱ͒, and ͑Ϫ ϱ, ϱ͒. NOTE The intervals ͑a, b͒, ͑Ϫ ϱ, b͒, and ͑a, ϱ͒ are open. The intervals ͓a, b͔, ͑Ϫ ϱ, b͔, and ͓a, ϱ͒ are closed. The interval ͑Ϫ ϱ, ϱ͒ is considered open and closed. The intervals ͑a, b͔ and ͓a, b͒ are neither open nor closed. ■ EXAMPLE 1 Intervals and Inequalities Write an inequality to represent each interval, and state whether the interval is bounded or unbounded. a. ͑Ϫ3, 5͔ b. ͑Ϫ3, ϱ͒ c. ͓0, 2͔ d. ͑Ϫ ϱ, ϱ͒ Solution a.