Question 1

Find a function r(t) that describes the line or line segment.
-The line through P(4, 9, 3) and Q(1, 6, 7)
A) r(t) = 
B) r(t) = 
C) r(t) = 
D) r(t) =

Accepted Answer

C

Question 2

Find a function r(t) that describes the line or line segment.
-The line segment from P(2, 7, 3) to Q(3, 1, 1)
A) r(t) =  ; 1 $\le$ t $\le$ 2
B) r(t) =  ; 1 $\le$t$\le$ 2
C) r(t) =  ; 0 $\le$ t$\le$1
D) r(t) =  ; 0 $\le$ t $\le$ 1

Accepted Answer

D

Question 3

Graph the curve described by the function, indicating the positive orientation.
-r(t) =  , for 0 $\le$ t $\le$ 2 $\pi$

A)

B)

C)

D)

Accepted Answer

B

Question 4

Graph the curve described by the function, indicating the positive orientation.
-r(t) = 2cos t i + 3j + 2 sin t k, for 0 $\le$ t $\le$2 $\pi$
A)

B)

C)

D)

Accepted Answer

The answer of Graph the curve described by the function,...

Question 5

Graph the curve described by the function. Use analysis to anticipate the shape of the curve before using a graphing utility.
-r(t) = 3 cos t i + 2 sin t j + cos 5t k, for 0 $\le$ t $\le$ 2$\pi$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the curve described by the function....

Question 6

Graph the curve described by the function. Use analysis to anticipate the shape of the curve before using a graphing utility.
-r(t) = cos 2t sin t i + sin 2t sin t j +  k, for 0 $\le$ t $\le$ 16

A)

B)

C)

D)

Accepted Answer

The answer of Graph the curve described by the function....

Question 7

Evaluate the limit. 
- = ( 7 cos ti+ 6 sin tj)
A) 7i
B) -6j
C) 6j
D) 7i - 6j

Accepted Answer

The answer of Evaluate the limit. 
- = ( 7...

Question 8

Evaluate the limit. 
-
A)

B)

C)

D)

Accepted Answer

The answer of Evaluate the limit. 
-
A)

B)

C)

D)...

Question 9

Find the domain of the vector-valued function.
-r(t) =  i +  j
A) t $\ge$ 5
B) $\ge$5
C)  < 5
D) t > 5

Accepted Answer

The answer of Find the domain of the vector-valued function.
-r(t)...

Question 10

Find the domain of the vector-valued function.
-r(t) = sin 3t i +  j
A) t $\ge$ 
B) t $\ge$ 0
C) t > 3
D)All real numbers

Accepted Answer

The answer of Find the domain of the vector-valued function.
-r(t)...

Question 11

Find a function r(t) that describes the curve where the surfaces intersect.
-z = 16; z =  + 
A) r(t) = 
B) r(t) = 
C) r(t) = 
D) r(t) =

Accepted Answer

The answer of Find a function r(t) that describes the...

Question 12

Find a function r(t) that describes the curve where the surfaces intersect.
- +  = 16; z = 2x + 3y
A) r(t) = 
B) r(t) = 
C) r(t) = 
D) r(t) =

Accepted Answer

The answer of Find a function r(t) that describes the...

Question 13

Verify that the curve r(t) lies on the surface. Give the name of the surface.  
-r(t) = (2t cos t)i + (2t sin t)j + 2t k;  +  = 
A)

B)

C)

D)

Accepted Answer

The answer of Verify that the curve r(t) lies on...

Question 14

Verify that the curve r(t) lies on the surface. Give the name of the surface.  
-r(t) =  ; z=  + 
A)

B)

C)

D)

Accepted Answer

The answer of Verify that the curve r(t) lies on...

Question 15

Differentiate the function.  
-r(t) = ( -7  - 6)i +  j
A)

B)

C)

D)

Accepted Answer

The answer of Differentiate the function.  
-r(t) = (...

Question 16

Differentiate the function.  
-r(t) = (cot t)i + (csc t)j
A)

B)

C)

D)

Accepted Answer

The answer of Differentiate the function.  
-r(t) = (cot...

Question 17

Find the unit tangent vector of the given curve. 
-r(t) = 3  i - 12  j + 4  k

A)

B)

C)

D)

Accepted Answer

The answer of Find the unit tangent vector of the...

Question 18

Find the unit tangent vector of the given curve. 
-r(t) = ( 6 - 2t)i + (2t - 9)j + ( 9 + t)k
A)

B)

C)

D)

Accepted Answer

The answer of Find the unit tangent vector of the...

Question 19

Find the unit tangent vector of the given curve. 
-r(t) = ( 6 + 10  )i + ( 9 + 11  )j + ( 1 + 2  )k

A)

B)

C) T = 10i + 11j + 2k
D)

Accepted Answer

The answer of Find the unit tangent vector of the...

Question 20

Find the unit tangent vector of the given curve. 
-r(t) =  i +  j - 12tk
A)

B)

C)

D)

Accepted Answer

The answer of Find the unit tangent vector of the...

Quiz 14: Vector-Valued Functions

Find a function r(t) that describes the line or line segment. -The line through P(4, 9, 3) and Q(1, 6, 7)

Find a function r(t) that describes the line or line segment. -The line segment from P(2, 7, 3) to Q(3, 1, 1)

Graph the curve described by the function, indicating the positive orientation. -r(t) = $Graph the curve described by the function, indicating the positive orientation. -r(t) = , for 0 \le t \le 2 \pi A) B) C) D)$ , for 0 $\le$ t $\le$ 2 $\pi$

Graph the curve described by the function, indicating the positive orientation. -r(t) = 2cos t i + 3j + 2 sin t k, for 0 $\le$ t $\le$ 2 $\pi$

Graph the curve described by the function. Use analysis to anticipate the shape of the curve before using a graphing utility. -r(t) = 3 cos t i + 2 sin t j + cos 5t k, for 0 $\le$ t $\le$ 2 $\pi$

Evaluate the limit. - = ( 7 cos ti+ 6 sin tj)

Evaluate the limit. -

Find the domain of the vector-valued function. -r(t) = $Find the domain of the vector-valued function. -r(t) = i + j A) t \ge 5 B) \ge 5 C) < 5 D) t > 5$ i + $Find the domain of the vector-valued function. -r(t) = i + j A) t \ge 5 B) \ge 5 C) < 5 D) t > 5$ j

Find the domain of the vector-valued function. -r(t) = sin 3t i + $Find the domain of the vector-valued function. -r(t) = sin 3t i + j A) t \ge B) t \ge 0 C) t > 3 D) All real numbers$ j

Find a function r(t) that describes the curve where the surfaces intersect. -z = 16; z = +

Find a function r(t) that describes the curve where the surfaces intersect. - + = 16; z = 2x + 3y

Verify that the curve r(t) lies on the surface. Give the name of the surface. -r(t) = (2t cos t) i + (2t sin t) j + 2t k; + =

Verify that the curve r(t) lies on the surface. Give the name of the surface. -r(t) = ; z= +

Differentiate the function. -r(t) = ( -7 - 6) i + j

Differentiate the function. -r(t) = (cot t) i + (csc t) j

Find the unit tangent vector of the given curve. -r(t) = 3 i - 12 j + 4 k

Find the unit tangent vector of the given curve. -r(t) = ( 6 - 2t) i + (2t - 9) j + ( 9 + t) k

Find the unit tangent vector of the given curve. -r(t) = ( 6 + 10 ) i + ( 9 + 11 ) j + ( 1 + 2 ) k

Find the unit tangent vector of the given curve. -r(t) = i + j - 12tk

Quiz 14: Vector-Valued Functions

Find a function r(t) that describes the line or line segment. -The line through P(4, 9, 3) and Q(1, 6, 7)

Find a function r(t) that describes the line or line segment. -The line segment from P(2, 7, 3) to Q(3, 1, 1)

Graph the curve described by the function, indicating the positive orientation. -r(t) = , for 0 ≤\le≤ t ≤\le≤ 2 π\piπ

Graph the curve described by the function, indicating the positive orientation. -r(t) = 2cos t i + 3j + 2 sin t k, for 0 ≤\le≤ t ≤\le≤ 2 π\piπ

Graph the curve described by the function. Use analysis to anticipate the shape of the curve before using a graphing utility. -r(t) = 3 cos t i + 2 sin t j + cos 5t k, for 0 ≤\le≤ t ≤\le≤ 2 π\piπ

Graph the curve described by the function. Use analysis to anticipate the shape of the curve before using a graphing utility. -r(t) = cos 2t sin t i + sin 2t sin t j + k, for 0 ≤\le≤ t ≤\le≤ 16

Evaluate the limit. - = ( 7 cos ti+ 6 sin tj)

Evaluate the limit. -

Find the domain of the vector-valued function. -r(t) = i + j

Find the domain of the vector-valued function. -r(t) = sin 3t i + j

Find a function r(t) that describes the curve where the surfaces intersect. -z = 16; z = +

Find a function r(t) that describes the curve where the surfaces intersect. - + = 16; z = 2x + 3y

Verify that the curve r(t) lies on the surface. Give the name of the surface. -r(t) = (2t cos t) i + (2t sin t) j + 2t k; + =

Verify that the curve r(t) lies on the surface. Give the name of the surface. -r(t) = ; z= +

Differentiate the function. -r(t) = ( -7 - 6) i + j

Differentiate the function. -r(t) = (cot t) i + (csc t) j

Find the unit tangent vector of the given curve. -r(t) = 3 i - 12 j + 4 k

Find the unit tangent vector of the given curve. -r(t) = ( 6 - 2t) i + (2t - 9) j + ( 9 + t) k

Find the unit tangent vector of the given curve. -r(t) = ( 6 + 10 ) i + ( 9 + 11 ) j + ( 1 + 2 ) k

Find the unit tangent vector of the given curve. -r(t) = i + j - 12tk

Graph the curve described by the function, indicating the positive orientation. -r(t) = $Graph the curve described by the function, indicating the positive orientation. -r(t) = , for 0 \le t \le 2 \pi A) B) C) D)$ , for 0 $\le$ t $\le$ 2 $\pi$

Graph the curve described by the function, indicating the positive orientation. -r(t) = 2cos t i + 3j + 2 sin t k, for 0 $\le$ t $\le$ 2 $\pi$

Graph the curve described by the function. Use analysis to anticipate the shape of the curve before using a graphing utility. -r(t) = 3 cos t i + 2 sin t j + cos 5t k, for 0 $\le$ t $\le$ 2 $\pi$

Find the domain of the vector-valued function. -r(t) = $Find the domain of the vector-valued function. -r(t) = i + j A) t \ge 5 B) \ge 5 C) < 5 D) t > 5$ i + $Find the domain of the vector-valued function. -r(t) = i + j A) t \ge 5 B) \ge 5 C) < 5 D) t > 5$ j

Find the domain of the vector-valued function. -r(t) = sin 3t i + $Find the domain of the vector-valued function. -r(t) = sin 3t i + j A) t \ge B) t \ge 0 C) t > 3 D) All real numbers$ j