5 Steps to a 5 AP Calculus BC 2019

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

8. Use Euler’s Method with a step size ofΔx= 0 .5 to computey(2), ify(x)isthe
   solution of the differential equation
   dy
   dx
   =y+xywith initial conditiony(0)=1.
   Answer: y(0)=1;y(0.5)= 1 + 0 .5(1+ 0 .1)= 1 .5;
   y(1)= 1. 5 + 0. 5 [ 1. 5 +(0.5)(1.5)]= 1. 5 + 0 .5[2.25]= 2. 625
   y(1.5)= 2. 625 + 0. 5 [ 2. 625 +(1)(2.625)]= 2. 625 + 2. 625 = 5. 25
   y(2)= 5. 25 + 0. 5 [ 5. 25 +(1.5)(5.25)]= 5. 25 + 0 .5[13.125]= 11. 8125

13.9 Practice Problems

Part A The use of a calculator is not

allowed.

1. Find the value ofcas stated in the Mean
   Value Theorem for Integrals forf(x)=x^3
   on [2, 4].


2. The graph offis shown in Figure 13.9-1.
   Find the average value off on [0, 8].

(4,4)

1

012345678

2

3

4

x

y

f

Figure 13.9-1

3. The position function of a particle moving
   on a coordinate line is given ass(t)=t^2 −
   6 t−7, 0≤t≤10. Find the displacement
   and total distance traveled by the particle
   from 1≤t≤4.


4. The velocity function of a moving particle
   on a coordinate line isv(t)= 2 t+ 1
   for 0≤t≤8. Att=1, its position is−4.
   Find the position of the particle att=5.

5.The rate of depreciation for a new piece of

equipment at a factory is given asp(t)=

50 t−600 for 0≤t≤10, wheretis

measured in years. Find the total loss of

value of the equipment over the first 5 years.

6.If the acceleration of a moving particle on a

coordinate line isa(t)=−2 for 0≤t≤4,

and the initial velocityv 0 =10, find the

total distance traveled by the particle during

0 ≤t≤4.

7.The graph of the velocity function of a

moving particle is shown in Figure 13.9-2.

What is the total distance traveled by the

particle during 0≤t≤12?

v(t)

v

t

20

10

–10

(^0) 1 2 3 4 5 6 7 8 9 10 11 12
Figure 13.9-2
8.If oil is leaking from a tanker at the rate of
f(t)= 10 e^0.^2 tgallons per hour, wheretis
measured in hours, how many gallons of oil
will have leaked from the tanker after the
first 3 hours?