5 Steps to a 5 AP Calculus BC 2019

420 STEP 5. Build Your Test-Taking Confidence

8. The correct answer is (D).
   Rewrite
   ∑∞

n= 1

3 n+^2

4 n

as

∑∞

n= 0

(3)^2

(

3 n

4 n

)

= 9

∑∞

n= 0

(

3

4

)n

= 9

(

1 +

3

4

+

(

3

4

) 2

+

(

3

4

) 3

+···

)

. Note

that 1+

3

4

+

(

3

4

) 2

+

(

3

4

) 3

is a geometric

series with a ratio of

3

4

. Thus the infinite series

is

a 1

1 −r

=

1

1 −

3

4

=4 and 9

∑∞

n= 0

(

3

4

)n

= 36.

9. The correct answer is (D).

The limh→ 0

ln(x+h−3)−ln(x−3)

h

is the

definition of the derivative for the function

y=ln(x−3); therefore, the limit is equal to

y′=

1

x− 3

.

10. The correct answer is (C).
    The Taylor polynomial of third degree about
    x=aisf(a)+f′(a)(x−a)+
    f′′(a)
    2!
    (x−a)^2 +
    f′′′(a)
    3!
    (x−a)^3. In this case, the third-degree
    polynomial aboutx=2is− 1 +(1)(x−2)−
    2
    2!
    (x−2)^2 +

6

3!

(x−2)^3 or− 3 +x−(x−2)^2 +

(x−2)^3.

11. The correct answer is (A).
    Note thatf′′>0 on the intervals (−∞,−4)
    and (0, 4). Thus, the graph of the functionf is
    concave up on these intervals. Similarly,
    f′′<0 and concave down on the intervals
    (−4, 0) and (4,∞). Therefore,fhas a point of
    inflection atx=−4, 0, and 4.


12. The correct answer is (C).

Rewrite

√

k

kn

as

k

(^12)
kn
or

1

kn−

12 , which is ap-series.

In order for the series to converge,

(

n−

1

2

)

must be greater than 1. Thus,n−

1

2

> 1

orn>

3

2

.

13. The correct answer is (C).
    Sincef′(x)>0,f(x) is increasing, and since
    f′′>0,f(x) is concave up. The graph of
    f(x) may look like the one below. The right
    Riemann sum contains the largest rectangles.

y f

0 12 x

Right Riemann Sum

Right

Trapezoidal

Midpoint

Left

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