Chapter 7 (Area/Volume)
Chapter 8 (The Fluff)
INTEGRALS
Chapter 10 (Conics+PP)
Chapter 11 (Vectors)
100
Determine the area of the region enclosed by
x = 1/2 y^2 − 3 and y = x − 1 .
What is 18?
100
The general formula for partial fractions with a Linear Factor (DOUBLE POINTS if answer includes Quadratic Factor)
What is (A)/(ax + b) and BONUS: (Bx+C)/(ax^2+bx+c)?
100
*Hint: secx + tanx over something else will help
int_0^(pi/4)sec(x)dx
What is
ln(sqrt2+1)?
100
For the given rectangular equation, write an equivalent polar equation.
xy = 7
r^2=7/(sinthetacostheta)
100
Find the resultant vector of u+v if u=<1,4,5> and v=<8,19,7>.
What is <9,23,12>?
200
(Calculator + 4 decimals) Determine the arc length and DOUBLE POINTS FOR SA around x-axis of
What is ~132.0350 units?
BONUS: What is 107845.3746 units?
200
Define interminate form and give 3 examples.
What is a form that can be evaluated using L'Hopitals?
Ex:
0/0, oo/oo,oo-oo,0^0,1^oo,oo^0,0^oo
200
int( 3 t + t^2 ) sin ( 2 t )dt
What is
− 1/2 ( 3 t + t^2 ) cos ( 2 t ) + 1/4 ( 3 + 2 t ) sin ( 2 t ) + 1/4 cos ( 2 t ) + C?
200
Name this figure and describe its function.
What is a Brachistochrone and it is the fastest way between two points?
200
Find the angle between vectors v=<3,-1,2> and
w = <1,-1,-2> and determine orthagonality.
What is
pi/2 and "orthagonal"?
300
100 points each for the volume of x2 from 0 to 3 revolved
a. around the x-axis
b. around the y-axis
c. around the line x=9
What is
a. 48.6?
b. (91*pi)/2
c.
(243pi)/2
300
intsin^2(theta)cos^2(theta)d theta
What is
1/8theta-1/32sin(4theta)+C?
300
intsqrt((w+3)^2+100dx
What is
10 | tan ( θ ) |?
300
Find the horizontal and vertical tangents of
x=3t+4
y=t2+t
Vertical: None
Horizontal: (-2.5,-0.25)
300
For 100 each, if u=<3,8,6> and v=<4,2,1> , find
a. u*v
b. u x v
c. v* (u x v)
What is
a. 34?
b. <-4,21,-26>?
c. 0?
400
This is the volume of a solid if every perpendicular cross section perpendicular to the y-axis is an isosceles right triangle with a leg in the coordinate plane.
What is 2/3 units2
400
intsqrt(x^2-4)/xdx
What is
sqrt(x^2-4)-2arcsec(x/2)+C?
400
int_2^oo9/(1-3z)^4dx
What is Converges and
1/125?
400
Find the rectangular equation for:
y=3sec(t)
x=6tan(t)
What is
y^2/9-x^2/36=1?
400
A Boeing 727 leaves the airport on a bearing of 45 degrees and travels 400 mph. The wind is blowing at a bearing of 135 degrees at a speed of 40 mph. What is the resultant speed in bearing?
What is ~401.995 mph at ~50.711 degrees?
500
A spherical tank 6 feet tall is filled with oil. This much work is required to pump all the oil out of a pipe 1 foot above the tank.
What is 24960 ft-lbs?
500
lim_(x->oo)(1+1/x)^x
What is y=e?
500
int8/(3x^3+7x^2+4x)dx
What is
2ln|x|+6ln|3x+4|−8ln|x+1|+C
500
Find the area of all three petals of
r=4sin3theta
What is
4pi?
500
Determine if the three vectors →a=⟨1,4,−7⟩⟩, b→=⟨2,−1,4⟩ and →c=⟨0,−9,18⟩ lie in the same plane or not.
What is a parallelepiped V=0 and yes they do?