26 STEP 2. Determine Your Test Readiness
- The area under the curvey=
√
xfromx= 1
tox=kis 8. Find the value ofk.
- For 0≤x≤ 3 π, find the area of the region
bounded by the graphs ofy=sinxand
y=cosx. - Let fbe a continuous function on [0, 6] that
has selected values as shown below:
x 0123456
f(x)12510172637
Using three midpoint rectangles of equal
widths, find an approximate value of
∫ 6
0
f(x)dx.
- Find the area of the region in the first
quadrant bounded by the curvesr=2 cosθ
andr=2 sinθ. - Determine the length of the curve defined
byx= 3 t−t^3 andy= 3 t^2 fromt=0to
t= 2.
Chapter 13
- If
dy
dx
=2 sinxand atx=π,y=2, find a
solution to the differential equation. - Water is leaking from a tank at the rate of
f(t)=10 ln (t+1) gallons per hour
for 0≤t≤10, wheretis measured in hours.
How many gallons of water have leaked from
the tank after exactly 5 hours? - Carbon-14 has a half-life of 5730 years. Ifyis
the amount of Carbon-14 present andy
decays according to the equation
dy
dt
=ky,
wherekis a constant andtis measured in
years, find the value ofk.
- What is the volume of the solid whose base is
the region enclosed by the graphs ofy=x^2
andy=x+2 and whose cross sections are
perpendicular to thex-axis are squares? - The growth of a colony of bacteria in a
controlled environment is modeled by
dP
dt
=. 35 P
(
1 −
P
4000
)
. If the initial
population is 100, find the population when
t=5.
55. If
dy
dx
=
−y
x^2
andy=3 whenx=2,
approximateywhenx=3 using Euler’s
Method with a step size of 0.5.
Chapter 14
- IfSis the sum of the series
∑∞
n= 1
(−1)n
2 n
andsn,
itsnthpartial sum, what is the maximum
value of|S−s 5 |?
- Determine whether the series
∑∞
n= 0
3
(n+1)^4
converges or diverges.
- For what values ofxdoes the series
x−
x^2
2
+
x^3
3
−
x^4
4
+···converge absolutely?
- Find the Taylor series expansion of f(x)=
1
x
about the pointx=2.
- Find the MacLaurin series fore−x^2.