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Vector-Valued Functions Quiz Flashcards | StudBud
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Vector-Valued Functions Quiz
Vector-Valued Functions Quiz
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1
Find the following limit:
< 1 , 0 , 0 >
< 0 , 0 , 0 >
< 0 , 0 , 1 >
< 1, 1, 1 >
2
find F'(x)
sinx
sinx - sin(-2)
sint
∫sinxdx
3
Evaluate the integral
< 4, 1/2 , -1 >
< 8 , 1/2 , -1 >
< 4, 1 , -1 >
< 4 , 1 , 1 >
4
BAD SCIENCE JOKE! What is the most difficult type of element to make jokes about?
Synthetic elements
Noble gases
Nonmetals
Metals
5
r(t) and s(t) are vector valued functions. What is r(t) x s(t) ?
complex valued function
real valued function
none of the above
vector valued function
6
r(t) and s(t) are vector valued functions. What is || r(t) || ?
vector valued function
none of the above
complex valued function
real valued function
7
Find the derivative of the dot product of
r
(t) = cos (t)
i
+ sin (t)
j
and
s
(t) =
i
+ t
j
in component form.
<-sin t, t cos t>
<cos t, t sin t>
<cos t, sin t^2>
<-sin t, sin t + t cos t>
8
Trivia question: For differentiable vector-valued functions "
r
", what is
always
true?
r × r' = <0, 0, 0>
r is orthogonal to r'
r ⋅ r' = 0
r is the only indefinite integral of r'
9
What is the domain of
r
(t)?
All reals except t = 0, 1
all reals except t = 0
all reals except t = 1
defined for all real numbers
10
Find r'(t) when r(t) = < 1/t , -1 , ln(t) >
< t2 , 0 , 1/t >
< -1 / t2 , 0 , 1/t >
< 1 / t2 , 0 , -1/t >
< -1 / t2 , 0 , et>
11
Find the dot product of
r
(t) = cos (t)
i
+ sin (t)
j
and
s
(t) =
i
+ t
j
in component form.
<-sin t, sin t + t cos t>
<-sin t, t cos t>
<cos t, sin t^2>
<cos t, t sin t>
12
Which common calculus rule is used to find the derivative of a cross-product or dot-product?
Product rule
Chain rule
Quotient rule
L'Hospital's rule
13
Which vector(s) is parallel to v = <1/2, 3/2>
<1,1>
<-1, 3>
<1, 3>
<-1,-3>
14
Find the tangent to the vector-valued function <cos t, sin t, t> at t = π.
<0, t, t>
<0, -t, t>
<-1, -t, π + t>
<-1, 0, π>
15
BAD KOREAN JOKE! Where should I always wear a suit?
Fayston
Apgujeong
Gwanghwamun
Jamsil
16
Find r( π/2 ) for r(t) = < tcos(t), tsin(t) >
< 0 , 1 >
< π/2 , 0 >
< 1, 0 >
< 0 , π/2 >
17
What is the angle between the vectors <-2, 2> and <2, -2>?
0
π/3
π/4
π/2
18
Find the speed of a particle on the path given by r(t) = < t , t
3
, 3t >
√11
√19
<1, 3, 3>
<3, 1, 3>
19
Describe the magnitude of the derivative of <t,t^2,t^3 >.
<1,2t,3t^2>
\sqrt{t^6+t^4+t^2}
\sqrt{9t^4+4t^2+1}
Undefined
20
Which rule accurately reflects derivatives of cross-products in 3-space? i.e. \frac{d}{dt}\left(r_1\times r_2\right)=
r_1\cdot\frac{d}{dt}r_2+r_2\cdot\frac{d}{dt}r_1
r_1\times\frac{d}{dt}r_2+r_2\times\frac{d}{dt}r_1
\frac{d}{dt}r_1\times\frac{d}{dt}r_2
r_1\times\frac{d}{dt}r_2-r_2\times\frac{d}{dt}r_1
21
Find the volume of the solid formed by revolving f(x) = √sinx about the x-axis from 0 to π
2π
0
1/2π
π
22
find ||r(t)|| given that r(t) = < tcos(t), tsin(t) >
| t |
t
1
t2
23
The projection of
u
onto
v
...
is orthogonal to v
is parallel to v
is orthogonal to u
is parallel to u
24
BAD KOREAN JOKE! Who is Batman's least favorite relative?
Brother
Nephew
Mother
Uncle
