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 extensively praised via a iteration of scholars and professors for its stable and powerful pedagogy that addresses the wishes of a extensive diversity of educating and studying kinds and environments. every one identify is only one part in a entire calculus direction application that conscientiously 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 advance detailed, readable fabrics for college kids that sincerely outline and show innovations and principles of calculus.
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X + 8 < 0 x−5 ■ Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. qxp 22 10/21/10 Chapter P 2:17 PM Page 22 Prerequisites A common application of inequalities is finding the domain of an expression that involves a square root, as shown in Example 8.
9. ) Choose x = 6. −x + 8 > 0 x−5 x 4 5 6 Choose x = 4. 9 7 8 9 Choose x = 9. −x + 8 < 0 x−5 ■ Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
When an equation contains two radicals, it may not be possible to isolate both. In such cases, you may have to raise each side of the equation to a power at two different stages in the solution, as shown in Example 12(b). STUDY TIP b. Ί2x Ϫ 5 Ϫ Ίx Ϫ 3 ϭ 1 Ί2x Ϫ 5 ϭ Ίx Ϫ 3 ϩ 1 2x Ϫ 5 ϭ x Ϫ 3 ϩ 2Ίx Ϫ 3 ϩ 1 2x Ϫ 5 ϭ x Ϫ 2 ϩ 2Ίx Ϫ 3 x Ϫ 3 ϭ 2Ίx Ϫ 3 2 x Ϫ 6x ϩ 9 ϭ 4͑x Ϫ 3͒ 2 x Ϫ 10x ϩ 21 ϭ 0 ͑x Ϫ 3͒͑x Ϫ 7͒ ϭ 0 xϪ3ϭ0 xϭ3 xϪ7ϭ0 xϭ7 Original equation Isolate Ί2x Ϫ 5. Square each side. Combine like terms.
Calculus I with Precalculus by Ron Larson