By Stefan Waner, Steven R. Costenoble
Take calculus into the true international with utilized CALCULUS. Authors Waner and Costenoble make utilized calculus effortless to appreciate and proper for your pursuits. And, this textbook interfaces along with your graphing calculator and your house spreadsheet software. Plus it comes with AppliedCalculusNOW. After an easy pre-test, the AppliedCalculusNOW on-line studying approach customizes the entire routines and sophistication info round your personal wishes. This version additionally comes with own coach with SMARTHINKING, which supplies you entry to one-on-one, on-line tutoring support with a professional within the topic. And it offers a digital research team, too?interact with the instruct and different scholars utilizing two-way audio, an interactive whiteboard for discussing the matter, and speedy messaging.
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- Calculus I
- The Mathematical Palette
- Simplicity with Respect to Certain Quadratic Forms
- A Book of Curves
Additional info for Finite mathematics
Example text
However, it looks rather like a quadratic. In fact, it is quadratic in x 2 , meaning that it is (x 2 ) 2 − 5(x 2 ) + 6 = y 2 − 5y + 6 where y = x 2 . The quadratic y 2 − 5y + 6 factors as y 2 − 5y + 6 = ( y − 3)( y − 2) so x 4 − 5x 2 + 6 = (x 2 − 3)(x 2 − 2) This is a sometimes useful technique. Our last example is here to remind you why we should want to factor polynomials in the first place. We shall return to this in Section 5. Example 4 Solving a Quadratic Equation by Factoring Solve the equation 3x 2 + 4x − 4 = 0.
Can’t we get a formula that gives the cumulative net income data exactly ? ” When we write a function in this form, the variable x is the independent variable and y is the dependent variable. We could also write the above function as f = x 2 − 25x + 15, in which case the dependent variable would be f. using Technology Evaluating a function can be tedious to do by hand, but various technologies make this task easier. See the Technology Guides at the end of the chapter to find out how to create a table like the one in Example 3, using a TI-83/84 or Excel.
5 4 What we mean by an “algebraic formula” is a formula in the coefficients using the operations of addition, subtraction, multiplication, division, and the taking of radicals. ” If you were a math major, you would eventually go on to study this under the heading of Galois Theory. 5 Both Abel (1802–1829) and Galois (1811–1832) died young. Abel died of tuberculosis at the age of 26, while Galois was killed in a duel at the age of 20. 5 EXERCISES Solve the equations in Exercises 1–12 for x (mentally, if possible).