Chapter 12 + 13
[12.3]
Set up the equation to find the arc length of the following curve:
r=2θ for 0≤θ≤2π
(I have to write it on the board because I will have to pay to include an image of the answer)
[14.2]
Find the velocity of the following function:
r(t)=<tsin(t),t2,tcos(t)>
r'(t)=<tcos(t)+sin(t),2t,-tsin(t)+cos(t)>
[15.5]
Find the gradient vector of:
f(x,y)=8xy-x2-2y2
nabla f=<-4,16>
[16.5]
Convert (-1,sqrt(3),2) into cylindrical and spherical cooardinates
cylindrical: (2,2π/3,2)
spherical: (2sqrt(2),π/4,2π/3)
What type of craft does Lorelei like to do?
Crochet
[13.3]
Compute the dot product between the 2 following vectors:
u=2j-4k and v=i-3j+2k
u.v=-14
[14.4]
Find the arc length of the following curve:
r(t)=<5t-1,t,4t+6> from 0≤t≤1
L=sqrt(42)
[15.5]
Find the direction derivative of nabla f=<-4,16> in the direction <sqrt(2)/2,sqrt(2)/2).
Duf=6sqrt(2)
[16.1]
Compute the double integral of y*exydA over the region R={(x,y)|0≤x≤2,0≤y≤7}
V=1/2[e14-15]
Where does Lorelei work (other than the university)?
Connecticut Agricultural Experiment Station
[13.4]
Find the torque produced by a 30N force applied at 30° to a 0.30m long wrench
τ=4.5 N*m
[14.3]
Describe the trajectory of the particle moving along the function:
r(t)=3cos(t)i+5sin(t)j+4cos(t)k
The particle moves on a sphere of radius 5 centered at the origin.
[15.6]
Find the linear approximation of ln(1+x+y) at (0,0) and estimate the value of f(0.07,-0.12)
L(x,y)+x+y
L(0.07,-0.12)=-0.05
[16.3]
Find the volume of the solid bounded by z=-16+x2+y2 and the xy-plane
V=128π
What other class has Lorelei LA'd before?
Physics with Dr. Poplawski
[13.3]
Find the work done by the force F=<2,2,3> along the segment P(0,0,1) to Q(0,6,6).
W=27J
[14.2]
Find the unit tangent vector of r(t) given:
r'(t)=<tcos(t)+sin(t),2t,-tsin(t)+cos(t)> at t=π
(Hint: I gave you the derivative of r)
I will write the answer on the board
[15.6]
Find the equation of the tangent plane to the surface:
xy+xz+yz=12 at the point (4,3,2)
5(x-4)+6(y-3)+7(z-2)=0
or
5x+6y+7z=52
[16.2]
Reverse the bounds of integration and evaluate:
(I will write on the board)
V=1/2
What is Lorelei's undergraduate degree and current degree program?
Undergrad: Forensic science with a conc. in chem
Grad: Chemistry
[13.4]
Find the vector orthogonal to the 2 vectors:
u=2j-4k and v=i-3j+2k
uxv=-8i+4j-2k
uxv=<-8,4,-2>
[14.3]
A baseball is hit at an initial velocity v(0)=<30,30> in m/s. Assume the only force is gravity (9.8m/s2). Find the velocity function of the ball.
v(t)=<30,-9.8t+30>
[15.7]
Find and describe the critical points of:
f(x,y)=4x2+y2-16x-6y+17
The critical point (2,3) is a local min
[16.4]
Find the average temperature of of the box D={(x,y,z)=0≤x≤2,0≤y≤2,0≤z≤2} with the temperature distribution T(x,y,z)=x2+xy+y2+z2
Average temperature=5
Lorelei has many pets (9). Guess the name of ONE of them.
Options: Mayvis, Tilly, Drucy, Sylvester, Lisle, Buford, Cheech, Smitty, the pleco that no one knows the name of, but it is probably the name of a vacuum brand.