5 Steps to a 5 AP Calculus BC 2019

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

(e)A possible graph is shown in

Figure 7.10-1.

(–1,0)

0

1

2

–1 1 2 3 4

possible

point of

inflection

y f

(4,2)

Figure 7.10-1

31. xlim→π
    2 x
    sinx

→

2 π

sinπ

→

2 π

0

. Note that
L’Hoˆpital’sRule does not apply, since the
form is not

0

0

. limx→π−
2 x
sinx
=∞, but

xlim→π+

2 x

sinx

=−∞; therefore, limx→π

2 x

sinx

does

not exist.

32. lim
    x→^12

3 − 6 x

4 x^2 − 1

→

0

0

, but byL’Hoˆpital’sRule

lim

x→^12

3 − 6 x

4 x^2 − 1

=lim

x→^12

− 6

8 x

=

− 6

4

=

− 3

2

33. To convertx^2 + 4 y^2 =4 to a polar
    representation, recall thatx=rcosθand
    y=rsinθ. Then, (rcosθ)^2 +4(rsinθ)^2 =4.
    Simplifying givesr^2 cos^2 θ+ 4 r^2 sin^2 θ= 4
    r=

2

√

cos^2 θ+4 sin^2 θ

=

2

√

1 +3 sin^2 θ