5 Steps to a 5 AP Calculus AB 2019 - William Ma

(Marvins-Underground-K-12) #1
MA 3972-MA-Book May 8, 2018 13:46

82 STEP 4. Review the Knowledge You Need to Score High


Part B Calculators are permitted.


  1. Enter into your calculatory 1 =| 2 x+ 4 |
    andy 2 =10. Locate the intersection
    points. They occur atx=−7 and 3. Note
    thaty 1 is belowy 2 fromx=−7to3.
    Since the inequality is less than or equal
    to, the solution is− 7 ≤x≤3. (See
    Figure 5.8-3.)


[−10, 10] by [−10, 15]
Figure 5.8-3


  1. Enter in your calculatory 1 =x^3 − 2 xand
    y 2 =1. Find the intersection points. The
    points are located atx=−1,− 0 .618, and
    1.618. Sincey 1 is abovey 2 in the
    intervals− 1 <x<− 0 .618 and
    x> 1 .618 excluding the endpoints, the
    solutions to the inequality are the
    intervals− 1 <x<− 0 .618 and
    x> 1 .618. (See Figure 5.8-4.)


[−2, 2] by [−2, 2]
Figure 5.8-4


  1. Enter tan


(
arccos


2
2

)
into your
calculator and obtain 1. (Note that
arccos


2
2

=


π
4
and tan

(
π
4

)
=1.)


  1. Factore^2 x− 6 ex+ 5 =0as
    (ex−5)(ex−1)=0. Thus, (ex−5)=0or
    (ex−1)=0, resulting inex=5 and
    ex=1. Taking the natural log of both


sides yields ln(ex)=ln 5≈ 1 .609 and
ln(ex)=ln 1=0. Therefore to the nearest
thousandth,x= 1 .609 or 0. (Note that
ln(ex)=x.)


  1. The equation 3 ln 2x− 3 =12 is
    equivalent to ln 2x=5. Therefore,
    eln 2x=e^5 ,2x=e^5 ≈ 148 .413159, and
    x≈ 74 .207.

  2. Entery 1 =
    2 x− 1
    x+ 1
    andy 2 =1 into your
    calculator. Note thaty 1 is belowy 2 = 1
    on the interval (−1, 2). Since the
    inequality is≤, which includes the
    endpoint atx=2, the solution is (−1, 2].
    (See Figure 5.8-5.)


[−4, 4] by [−4, 7]
Figure 5.8-5


  1. Examinef(−x) and f(−x)=−2(−x)^4
    +(−x)^2 + 5 =− 2 x^4 +x^2 + 5 = f(x).
    Therefore, f(x) is an even function.
    (Note that the graph of f(x)is
    symmetrical with respect to they-axis;
    thus, f(x) is an even function.) (See
    Figure 5.8-6.)


[−4, 4] by [−4, 7]
Figure 5.8-6


  1. Entery 1 =x^4 − 4 x^3 into your calculator
    and examine the graph. Note that the
    graph is decreasing on the interval
    (−∞, 3) and increasing on (3,∞). The
    function crosses thex-axis at 0 and 4.
    Thus, the zeros of the function are 0 and

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