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

MA 3972-MA-Book May 7, 2018 9:52

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

6.4 Rapid Review

1. Findf(2) and limx→ 2 f(x) and determine iffis continuous atx=2. (See Figure 6.4-1.)

Answer: f(2)=2, lim

x→ 2

f(x)=4, and fis discontinuous atx=2.

20

2

4

(4, 2)

y

x

f(x)

(2, 2)

Figure 6.4-1

2. Evaluate limx→a
   x^2 −a^2
   x−a

.

Answer: xlim→a

(x+a)(x−a)

x−a

= 2 a.

3. Evaluate limx→∞
   1 − 3 x^2
   x^2 + 100 x+ 99

.

Answer: The limit is−3 since the polynomials in the numerator and denominator have

the same degree.

4. Determine iff(x)=

{

x+6 forx< 3

x^2 forx≥ 3

is continuous atx=3.

Answer: The functionfis continuous sincef(3)=9, limx→ 3 +f(x)=limx→ 3 − f(x)=9, and

f(3)=limx→ 3 f(x).

5. Iff(x)=

{

ex forx= 0

5 forx= 0

, find limx→ 0 f(x).

Answer: limx→ 0 f(x)=1 since limx→ 0 + f(x)=xlim→ 0 −f(x)=1.

6. Evaluate limx→ 0
   sin 6x
   sin 2x

.

Answer: The limit is

6

2

=3 since limx→ 0

sinx

x

=1.

7. Evaluate lim
   x→ 5 −

x^2

x^2 − 25

.

Answer: The limit is−∞since (x^2 −25) approaches 0 through negative values.