Algebra/Trig Review - Pauls Online Math Notes - Lamar University

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Algebra/Trig ReviewFrom this we see that the solution to this inequality is −∞ < x < − 2 and 5 < x
Algebra/Trig Review3.23x−2x− 11 > 0SolutionThis one is a little different, but not really more difficult. The quadratic doesn’tfactor and so we’ll need to use the quadratic formula to solve for where it is zero.Doing this gives1±34x =3Reducing to decimals this is x = 2.27698 and x = − 1.61032. From this point on it’sidentical to the previous two problems. In the number line below the dashed lines areat the approximate values of the two numbers above and the inequalities show thevalue of the quadratic evaluated at the test points shown.From the number line above we see that the solution is⎛1+34 ⎞⎜ , ∞3 ⎟.⎝ ⎠⎛ 1−34 ⎞⎜−∞,3 ⎟⎝ ⎠and4.x − 3 ≥ 0x + 2SolutionThe process for solving inequalities that involve rational functions is nearly identicalto solving inequalities that involve polynomials. Just like polynomial inequalities,rational inequalities can change sign where the rational expression is zero. However,they can also change sign at any point that produces a division by zero error in therational expression. A good example of this is the rational expression 1 x . Clearly,there is division by zero at x = 0 and to the right of x = 0 the expression is positiveand to the left of x = 0 the expression is negative.It’s also important to note that a rational expression will only be zero for values of xthat make the numerator zero.© 2006 Paul Dawkins 39http://tutorial.math.lamar.edu/terms.aspx
Page 1 and 2: Algebra/Trig ReviewIntroductionThis
Page 3 and 4: Algebra/Trig ReviewSimplifying Rati
Page 5 and 6: Algebra/Trig Review1 1 1 13− −
Page 7 and 8: Algebra/Trig Review⎧33 −8xif x
Page 9 and 10: Algebra/Trig ReviewTo convert radic
Page 11 and 12: Algebra/Trig ReviewSo, what do we d
Page 13 and 14: Algebra/Trig Review( )2f x =− x +
Page 15 and 16: Algebra/Trig Review⎛ f ⎞⎜ ⎟
Page 17 and 18: Algebra/Trig ReviewYou can memorize
Page 19 and 20: Algebra/Trig Review6.SolutionIn thi
Page 21 and 22: Algebra/Trig Review2. ( ) 2y = x+ 3
Page 23 and 24: Algebra/Trig ReviewWe could also us
Page 25 and 26: Algebra/Trig Review26. ( ) 2x+ y+ 5
Page 27 and 28: Algebra/Trig Review2 29. ( x+ 1 ) (
Page 29 and 30: Algebra/Trig Review12. y = xSolutio
Page 31 and 32: Algebra/Trig ReviewComplex numbers
Page 33 and 34: Algebra/Trig ReviewFrom this we see
Page 35 and 36: Algebra/Trig ReviewSo, now that we
Page 37: Algebra/Trig ReviewSo, the two inte
Page 41 and 42: Algebra/Trig ReviewIn this case we
Page 43 and 44: Algebra/Trig ReviewSolutionThis one
Page 45 and 46: Algebra/Trig Review4x+ 534x−2x
Page 47 and 48: Algebra/Trig ReviewRemember how the
Page 49 and 50: Algebra/Trig ReviewFrom this unit c
Page 51 and 52: Algebra/Trig ReviewNow, if we remem
Page 53 and 54: Algebra/Trig ReviewTo do this probl
Page 55 and 56: Algebra/Trig ReviewIf ω > 1we can
Page 57 and 58: Algebra/Trig ReviewIn the case of t
Page 59 and 60: Algebra/Trig ReviewSolutionCotangen
Page 61 and 62: Algebra/Trig Review2x = 1 ( + ( x))
Page 63 and 64: Algebra/Trig Reviewdetermine what t
Page 65 and 66: Algebra/Trig Review3Now, there are
Page 67 and 68: Algebra/Trig Review4π2πn− 4x= +
Page 69 and 70: Algebra/Trig ReviewSince we want th
Page 71 and 72: Algebra/Trig Reviewπw= + 2 π n, n
Page 73 and 74: Algebra/Trig ReviewI didn’t put i
Page 75 and 76: Algebra/Trig ReviewSo, using our ca
Page 77 and 78: Algebra/Trig ReviewThere’s anothe
Page 79 and 80: Algebra/Trig ReviewFrom this we can
Page 81 and 82: Algebra/Trig Review5.⎛cos cos⎜
Page 83 and 84: Algebra/Trig Reviewx3. List as some
Page 85 and 86: Algebra/Trig ReviewBasic Logarithmi
Page 87 and 88: Algebra/Trig ReviewSolutionlog b xb
Page 89 and 90:
Algebra/Trig ReviewThe domain y = l
Page 91 and 92:
Algebra/Trig ReviewIn each of the e
Page 93 and 94:
Algebra/Trig Review1−3z7 + 15e= 1
Page 95 and 96:
Algebra/Trig ReviewThe first step i
Page 97 and 98:
Algebra/Trig Reviewx 2= e1−x2x= e
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Algebra/Trig Review - Pauls Online Math Notes - Lamar University

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