Flashcards
Calc Exam 2
Cards in this deck (126)
- 1—Elliptic Paraboloid
- 2—Ellipsoid
- 3—Hyperboloid of 2 sheets
- 412Parallel to y-axis
- 515Ellipsoid
xy-circle
yz-ellipse
xz-ellipse
- 618hyperbolic paraloid
xy-line
xz-parabola
yz-parabola - 729
- 832
- 933
- 1045
- 111one
- 124xz plane
- 137
- 149
- 1511
- 1615
- 1721
- 1823
- 1925
- 2038All real except t=1, -2
- 21410≤t≤2
- 229<-sint, 2t, cost>
- 2313
- 2417r'(t) = <1,6,3>
- 2523<(2/3), (2/3), (1/3)>
- 2625
- 2731
- 2849
- 2950
- 3060
- 3162
- 3273i hat
- 3374<0.608, 0, 2>
- 349v(t)=<6t, 8t>
speed=10t
a(t)=<6,8>
- 3513a. 8
b. <-8sint, -8cost> - 3616
- 3721a. [0, 1]
b. r'(t) = <1, 2t>
R'(t) = <2, 8t>
- 3824a. [1, 10]
b. r'(t) = <-e^t, e^-t>
R'(t) = <-1, t^-2>
- 3935v(t) = <2, t+3>
r(t) = <2t, 0.5t^2 + 3t>
- 4036
- 4138
- 4241a. v(t) = <30, 6-9.8t>
r(t) = <30t, 6t-4.9t^2>
c. t = 1.22s
deltax = 36.73m
ymax = 1.84m
- 4344a. v(t) = <132, -32t>
r(t) = <132t, -16t^2+10>
c. t=0.79s
deltax=104.36ft
d. 10ft - 4451a. v(t) = <200, 200, -9.8t>
r(t) = <200t, 200t, -4.9t^2+1>
c. t=0.45s
range=127.78m
d. 1m
- 4554a. v(t) = <30, 30+5t, 80-32t>
r(t) = <30t, 30t+2.5t^2, 80t-16t^2+3>
c. t=5.037s
range=262.43ft
d.103ft
- 46—v(t)=
r(t)=
theta=27.38 degrees, 62.62 degrees
- 47—a. v(t)=<-asint, bcost>
|v(t)|=sqrt (a^2sin^2t + b^2cos^2t)
c. yes, more curved=slower it moves
d. b/a & a/b
- 485. An object moves on a trajectory given by r(t)=<10cos2t, 10sin2t> for 0≤t≤pi. h how far does it travel?20pi
- 498. Is the curve r(t)= parameterized by its arc length? Explain.yes, r(t) is para by its arc length bc s(t)=t: para t also measure arch length s.
- 5095
- 51128pi
- 52155sqrt34
- 53184
- 54213/2
- 552426t
52
- 5626e^t (sqrt3)
sqrt3 - 5733yes s(t)=t
- 5836No
- 5912t-hat=<-sint, -cost>
k=1/2
- 6015
- 6118
- 62211/3
- 63223/25
- 6423
- 65241/2
- 6627T-hat=
N-hat=<-sint, -cost>
=0
- 6730
- 6833
- 6936aT=0
aN=10
- 7039
- 71—
- 723{(x,y): x≠0 and y≠0}
- 734{(x,y): y≤x}
- 74—a. 1300ft
b. katie experiences greater elevation change. she is 100ft higher than zeke
- 75—circles of different radi along the z-axis
- 7615D=R^2
- 7718D={(x,y): x^2+y^2>25}
- 7821{(x,y): x^2>y}
- 7927D=R^2
R=R
Hyperbolic paraboloid
- 8030{(x,y): -x^2-y^2≤1}
R=[0, 1]
Half an ellipsoid
- 8133{(x,y): -2≤x≤2, -inf
- 82—a. A
b. D
c. B
d. C
- 8336
- 8440
- 85—a. ERA=0.964
b. 7.2
c. i=3e. i has to be 3e to get an ERA of 3
- 86—
- 873polynomials of n-values are continuous on all of R^n, limits of polynomials can be evaluated with direct substitution
- 885If the function is discontinuous and the left differs from the right, the limit DNE
- 89121≠-1
- 901527
- 9118ln(2e)
- 92216
- 93291≠-1
- 94332≠0
- 9536R^2
- 9639{(x,y): x≠0}
- 9745R^2
- 9848R^2
- 993a. negative
b. negative
c. negative
d. positive
- 1004fx(x,y)=12x^5 + 2y
fy(x,y)=8y^7 + 2x - 1015fx(x,y)=6xy
fy(x,y)=3x^2 - 1027fxy=0=fyx
- 1038fxy=e^y=fyx
- 10416fx(x,y)=12x^2 y^2 + 6xy^3
fy(x,y)=8x^3y + 9x^2y^2
- 10519
- 10622d
- 10726f
- 108—a. Vh=pi*h(2r-h)
Vr=pi*h^2
b. h=0.8r
c. h=sqrt(1/pi)
d. h=2r
- 10973Ut=-16e^(-4t) cos(2x)=Uxx
- 11074Ut=-10e^-t sinx=Uxx
- 11175Ut=-a^2 Ae^(-1^2 t) cos(ax)=Uxx
- 112—a. Zx=1/y^2
Zy=(-2x)/y^3
c. as x increases, z increases
d. as y increases, z decreases when y>0
as y increases, z increases when y<0
z is undefined @ y=0
- 11392tsin(4t^3)+12t^4 cos(4t^3)
- 11411-sin(t)sin(3t^4) + 12t^3 cos(t)cos(3t^4)
- 115120
- 11616f
- 11722Zs=cos(s+t)cos(2s-2t)-2sin(s+t)sin(2s-2t)
Zt=cos(s+t)cos(2s-2t)+2sin(s+t)sin(2s-2t)
- 11824Zs=2(s+t)^10 stcos(s^2 t(s+t)^10)) + 10(s+t)^9(s^2 t)cos(s^2 t(s+t)^10)
Zt=s^2 (s+t)^10 cos(s^2 t(s+t)^10)) + 10(s+t)^9(s^2 t)cos(s^2 t(s+t)^10) - 119—a. 2pi*r(t) h(t) r'(t) + pi(r(t))^2 h'(t)
b. 0
c. As t increases, volume remains constant
- 12043fss=2(3s+t)
fst=2(s-t)
ftt=-2(s+3t)
- 12146fss=2(2s^2+1)e^(s^2 -3t^2)
fst=-12ste^(s^2 -3t^2)
ftt=-6(-6t^2 +1)e^(s^2 -3t^2) - 122510
- 12353-z^2 /x^2
- 124—E'(t)= mx'(t)x''(t) + my'(t)y''(t) + mgy'(t)
0
The rate of change of energy of the projectile is constant
- 125—a. ax^(a-1) y^(1-a)
(1-a) (x^a /y^a)
b. (-ay)/((1-a)x)
c. -1
- 126—
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- Flashcards on Calc Exam 2, created by Esther Mun on 08/03/2022.
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- Esther Mun
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