By Stefan Waner
Take calculus into the true international with utilized CALCULUS. Authors Waner and Costenoble make utilized calculus effortless to appreciate and correct in your pursuits. And, this textbook interfaces together with your graphing calculator and your place spreadsheet application. Plus it comes with AppliedCalculusNOW. After an easy pre-test, the AppliedCalculusNOW on-line studying procedure customizes the entire routines and sophistication info round your personal wishes. This version additionally comes with own educate with SMARTHINKING, which provides you entry to one-on-one, on-line tutoring support with knowledgeable within the topic. And it delivers a digital learn staff, too-interact with the train and different scholars utilizing two-way audio, an interactive whiteboard for discussing the matter, and quick messaging.
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Extra resources for Applied Calculus, Enhanced Review 4th Edition (with CengageNOW, Personal Tutor Printed Access Card)
Airlines’ cumulative net income from Jan. 2000 because it uses an algebraic formula to model—or mathematically represent (approximately)—the cumulative net income. The particular kind of algebraic model we used is called a quadratic model (see the end of this section for the names of some commonly used models). ■ Q: The values of f(x) are close to but don’t all equal those of P(x). Is this the best we can do with an algebraic model? Can’t we get a formula that gives the cumulative net income data exactly ?
Let’s look at these equations one degree at a time. 24 Chapter 0 Algebra Review Solution of Linear Equations By deﬁnition, a linear equation can be written in the form ax + b = 0 a and b are ﬁxed numbers with a = 0. Solving this is a nice mental exercise: Subtract b from both sides and then divide by a, getting x = −b/a. Don’t bother memorizing this formula; just go ahead and solve linear equations as they arise. If you feel you need practice, see the exercises at the end of the section. 1 The solutions of this equation are also called the roots of ax 2 + bx + c .
17 2 6 − 4 =0 x3 x 109. 3 Multiplying and Factoring Algebraic Expressions Multiplying Algebraic Expressions Distributive Law The distributive law for real numbers states that a(b ± c) = ab ± ac (a ± b)c = ac ± bc for any real numbers a, b, and c. quick Examples 1. 2(x − 3) is not equal to 2x − 3 but is equal to 2x − 2(3) = 2x − 6. 2. 3. 4. 5. 6. x(x + 1) = x 2 + x 2x(3x − 4) = 6x 2 − 8x (x − 4)x 2 = x 3 − 4x 2 (x + 2)(x + 3) = (x + 2)x + (x + 2)3 = (x 2 + 2x) + (3x + 6) = x 2 + 5x + 6 (x + 2)(x − 3) = (x + 2)x − (x + 2)3 = (x 2 + 2x) − (3x + 6) = x 2 − x − 6 There is a quicker way of expanding expressions like the last two, called the “FOIL” method (First, Outer, Inner, Last).
Applied Calculus, Enhanced Review 4th Edition (with CengageNOW, Personal Tutor Printed Access Card) by Stefan Waner