By Ron Larson
CALCULUS I WITH PRECALCULUS, brings you up to the mark algebraically inside precalculus and transition into calculus. The Larson Calculus software has been greatly praised through a new release of scholars and professors for its stable and powerful pedagogy that addresses the wishes of a large diversity of educating and studying types and environments. each one identify is only one part in a accomplished calculus path software that conscientiously integrates and coordinates print, media, and expertise items for profitable instructing and studying. One basic goal guided the authors in penning this e-book: to enhance unique, readable fabrics for college students that basically outline and show recommendations and ideas of calculus
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Additional info for Calculus I with precalculus : a one-year course
The algebraic equations on the papyrus were written in words. D. 250, is often called the Father of Algebra. He was the first to use abbreviated word forms in equations. x 3x ϩ ϭ2 3 4 x 3x ͑12͒ ϩ ͑12͒ ϭ ͑12͒2 3 4 4x ϩ 9x ϭ 24 24 xϭ 13 Write original equation. Multiply each term by the LCD of 12. Divide out and multiply. Combine like terms and divide each side by 13. Check x 3x ϩ 3 4 24͞13 3͑24͞13͒ ϩ 3 4 8 18 ϩ 13 13 26 13 ϭ2 Write original equation. ϭ2 Substitute 24 13 for x. ϭ2 Simplify. ϭ2 Solution checks.
The equation has two solutions: xϭ Ϫ3 ϩ 3Ί5 2 and xϭ Ϫ3 Ϫ 3Ί5 . 2 Check these in the original equation. EXAMPLE 9 The Quadratic Formula: One Solution Use the Quadratic Formula to solve 8x2 Ϫ 24x ϩ 18 ϭ 0. Solution 8x2 Ϫ 24x ϩ 18 ϭ 0 4x2 Ϫ 12x ϩ 9 ϭ 0 Write original equation. Divide out common factor of 2. xϭ Ϫb ± Ίb2 Ϫ 4ac 2a Quadratic Formula xϭ Ϫ ͑Ϫ12͒ ± Ί͑Ϫ12͒2 Ϫ 4͑4͒͑9͒ 2͑4͒ b ϭ Ϫ12, and c ϭ 9. xϭ 12 ± Ί0 3 ϭ 8 2 Substitute a ϭ 4, Simplify. This quadratic equation has only one solution: x ϭ 32.
81. 83. 85. 87. 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. 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 141. x ϭ x 2 ϩ x Ϫ 3 142. x 2 ϩ 6x ϭ 3x ϩ 18 143. 144. x Ϫ 10 ϭ x 2 Ϫ 10x 93. 5 ϭ 0 94. 193 ϭ 0 95. 422x 2 Ϫ 506x Ϫ 347 ϭ 0 96. 651 ϭ 0 In Exercises 97–104, solve the equation using any convenient method. 98.
Calculus I with precalculus : a one-year course by Ron Larson