By Ron Larson
CALCULUS I WITH PRECALCULUS, brings you in control algebraically inside of precalculus and transition into calculus. The Larson Calculus application has been broadly praised by way of a new release of scholars and professors for its reliable and powerful pedagogy that addresses the wishes of a vast diversity of educating and studying kinds and environments. every one identify is only one part in a finished calculus direction application that rigorously integrates and coordinates print, media, and know-how items for profitable educating and studying. One fundamental goal guided the authors in penning this booklet: to improve detailed, readable fabrics for college students that basically outline and show recommendations and ideas of calculus.
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Extra resources for Calculus I with Precalculus
Subtract 2x from each side. Subtract 2 from each side. Use a graphing utility to graph y1 ϭ 1 Ϫ 32 x and y2 ϭ x Ϫ 4 in the same viewing window. 3, you can see that the graphs appear to intersect at the point ͑2, Ϫ2͒. Use the intersect feature of the graphing utility to confirm this. The graph of y1 lies above the graph of y2 to the left of their point of intersection, which implies that y1 Ն y2 for all x Յ 2. Divide each side by Ϫ5 and reverse the inequality. The solution set is all real numbers that are less than or equal to 2, which is denoted by ͑Ϫ ϱ, 2͔.
32͑z ϩ 5͒ Ϫ 14͑z ϩ 24͒ ϭ 0 24. 40͑100 Ϫ x͒ ϭ 50 In Exercises 25–38, solve the equation and check your solution. ) In Exercises 67–76, solve the quadratic equation by completing the square. 25. x ϩ 8 ϭ 2͑x Ϫ 2͒ Ϫ x 26. 8͑x ϩ 2͒ Ϫ 3͑2x ϩ 1͒ ϭ 2͑x ϩ 5͒ 100 Ϫ 4x 5x ϩ 6 27. ϭ ϩ6 3 4 17 ϩ y 32 ϩ y 28. ϩ ϭ 100 y y 67. 69. 71. 73. 75. x 2 ϩ 4x Ϫ 32 ϭ 0 x 2 ϩ 12x ϩ 25 ϭ 0 8 ϩ 4x Ϫ x 2 ϭ 0 2x 2 ϩ 5x Ϫ 8 ϭ 0 5x2 Ϫ 15x ϩ 7 ϭ 0 56. 58. 60. 62. 64. 66. x 2 ϭ 32 9x 2 ϭ 36 ͑x ϩ 13͒2 ϭ 25 ͑x Ϫ 5͒2 ϭ 30 ͑2x ϩ 3͒2 Ϫ 27 ϭ 0 ͑x ϩ 5͒2 ϭ ͑x ϩ 4͒ 2 55.
89. 91. 2x 2 ϩ x Ϫ 1 ϭ 0 2 ϩ 2x Ϫ x 2 ϭ 0 x 2 ϩ 14x ϩ 44 ϭ 0 12x Ϫ 9x 2 ϭ Ϫ3 9x2 ϩ 24x ϩ 16 ϭ 0 28x Ϫ 49x 2 ϭ 4 8t ϭ 5 ϩ 2t 2 ͑ y Ϫ 5͒2 ϭ 2y 78. 80. 82. 84. 86. 88. 90. 92. 25x 2 Ϫ 20x ϩ 3 ϭ 0 x 2 Ϫ 10x ϩ 22 ϭ 0 6x ϭ 4 Ϫ x 2 4x 2 Ϫ 4x Ϫ 4 ϭ 0 16x 2 Ϫ 40x ϩ 5 ϭ 0 3x ϩ x 2 Ϫ 1 ϭ 0 25h2 ϩ 80h ϩ 61 ϭ 0 ͑57x Ϫ 14͒2 ϭ 8x In Exercises 93–96, use the Quadratic Formula to solve the equation. ) 93. 5 ϭ 0 94. 193 ϭ 0 95. 422x 2 Ϫ 506x Ϫ 347 ϭ 0 96. 1x2 In Exercises 97–104, solve the equation using any convenient method.
Calculus I with Precalculus by Ron Larson