Flashcards
Calc Exam 3
Cards in this deck (96)
- 13Direction of gradient vector is the direction of the steepest slope.
- 24Magnitude of the gradient vector is the maximum rate of change in a direction.
- 37-2
- 413<12, 10>
- 516<4/sqrt7, 1/sqrt7>
- 6192e^-9<1, -4>
- 721-6
- 82218
- 928-1/3
- 1031a. SA=1/sqrt65 <1,8>
SD=-1/sqrt65 <1,8>
b. <-8, 1>
- 1132a. SA=1/5 <4,3>
SD=-1/5 <4,3>
b. <-3, 4> - 1259a. <2, 0, 32>
b. 1/sqrt257 <1, 0, 16>
c. 2sqrt257
d. 34/sqrt2
- 1360a.<0, 12, -1>
b. 1/sqrt145 <0, 12, -1>
c. sqrt145
d. 13/sqrt2 - 1463a. <-0.5, -1, 0.5>
b. 1/sqrt6 <-1, -2, 1>
c. (sqrt6)/2
d. -.5 - 1566a. <1/3, -4/9, 1/9>
b. 1/sqrt26 <3, -4, 1>
c. sqrt(26/81)
d. -7/27 - 16132x+y+z=4
4x+y+z=7
- 17142x+4z=6
-2x+4z=6 - 18166x+8y-10z=0
-8x-6y-10z=0 - 1920z=y+2
z=5x+2 - 2023-0.5x-2/3y-2sqrt(3)z=2
x-2y+2sqrt(14)z=2 - 2127z=7/25x-1/25y-2/5
z=-7/25x+1/25y+6/5 - 2229z=1/2x+1/2y-1+pi/4
- 2330z=x+y
- 2433a. 4x+y-6
b. 5.39
- 2534a. 8x-64y+144
b. -117.2 - 26%change=(v2-v1)/v1 *100-0.843%
- 27—a. 0.0365
b. 0.068>0.025, so when theta=pi/20, the change in c is greater in magnitude.
- 2814()
- 2921(3,0)
(-15,6) - 3027(0,0) Saddle Point
(1,1)u(-1,-1) Local min
- 3131(2,0) Local min
- 3233C(0,0)-Saddle Point
C(sqrt(1/2),sqrt(1/2))-local max
C(-sqrt(1/2),sqrt(1/2))-local min
C(-sqrt(1/2),-sqrt(1/2))-local max
C(sqrt(1/2),-sqrt(1/2))-local min - 334316x16x32
v=8192in^3
- 34452m x 2m x 1m
- 35470=f(0,1) Absolute Min
9=f(0,-2) Absolute Max
- 36550=f(0,0) Absolute Min
7/8=f(1/sqrt2, sqrt2) Absolute Max - 3763P(4/3, 2/3, 4/3)
- 3866xx
- 39—x=y=z=200/3
- 409Absolute Min = -2 @(-1,-1)
Absolute Max = 2 @(1,1)
- 4113Absolute Min = e^3
@(sqrt3,sqrt3)U(-sqrt3,-sqrt3)
Absolute Max = e^-9
@(3,-3)U(-3,3) - 4218Absolute Min = 3sqrt3/2sqrt2
@(sqrt3,(sqrt3)/2,sqrt3/sqrt2)
U(-sqrt3,-(sqrt3)/2,sqrt3/sqrt2)
U(-sqrt3,(sqrt3)/2,-sqrt3/sqrt2)
U(sqrt3,-(sqrt3)/2,-sqrt3/sqrt2)
Absolute Max = -3sqrt3/2sqrt2
@(-sqrt3,(sqrt3)/2,sqrt3/sqrt2)
U(-sqrt3,-(sqrt3)/2,-sqrt3/sqrt2)
U(sqrt3,-(sqrt3)/2,sqrt3/sqrt2)
U(sqrt3,(sqrt3)/2,-sqrt3/sqrt2) - 4323Absolute Min = -10
@(-5,0,0)
Absolute Max = 29/2
@(2,0,sqrt(21/2))U(2,0,-sqrt(21/2)) - 442718x18x36
V=11664 in^3
- 4532d=1
P(-112/49,32/7,1/7) - 4633P(-3/17,29/17,-3)
- 47—2x2x1 m
- 4863P(4/3,2/3,4/3)
- 4988
- 50932/3
- 511238/3
- 521510-2e
- 53161/2
- 542614/3
- 55294/3
- 56334/11
- 5741e^2-3
- 5844h
- 59471/(2ln2)
- 60112
- 61138/3
- 62162ln2-1
- 6317e-1
- 64212
- 6528
- 6629
- 6732
- 6833
- 69432
- 705132
- 7157
- 7259
- 731164pi/3
- 741420pi*ln(10)-18pi
- 75157pi/2
- 76168pi
- 7721128pi
- 78230
- 7926-pi/e^9 + pi
- 8030128pi
- 81—pi
- 82—8pi
- 83—2pi((-15+7sqrt7)/3)
- 84103
- 85112/pi
- 86—8
- 87—42sqrt3/10
- 882232pi/3 (sqrt2-1)
- 892327pi/2
- 90—5/12
- 91—
- 9239256/9
- 9342oop
- 9445.5ln8 - (7/16)e
- 95—2/3
- 96—8/pi
