# MATH 260 Kalamazoo Valley Community College Vector Functions Solved Practice

Description

I need help with the MATH 260 homework attached.

Name
Math 260
Summer 2021
Homework Set 2
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1. Identify the surface with equation

!
2. Evaluate lim
t 0
1
2t + 5
i+
sin t
t
2
x
j + e3t k
4y
2
+ 9z
2
+ 36 = 0.
(4 pts.)

.
(4 pts.)
2
3. Find a vector function that represents the curve of intersection of the paraboloid z = x
2
and the cylinder x
+y
2
= 16.
(4 pts.)
1
+y
2
4. Consider the vector function
r(t) =
2
5t; 3; t
. Find the unit tangent vector
T (t) when t = 1.
(4 pts.)
5. Solve the initial value problem.
r0 (t) = e2t i + 6t2 j
2
k; r(0) = 3i + 4j
(sin t)
k
5
(4 pts.)
6. Set up, but do not evaluate, an integral representing the arc length of the curve
r(t) =
sin t; e
2t
; ln t , where 1

t
2.
7. Find the curvature of the curve given by
(5 pts.)
r(t) = h4 sin t;
3
i
t; 4 cos t .
(5 pts.)
8. Determine the domain of the function f (x; y) =
9. Consider the function f (x;
2
y) = x
2
+ 4y .
ln(2
2
x
+y
x)
2
16
.
Draw a contour map showing the level curves
corresponding to f (x; y) = k, where k = 4; k = 9 and k = 16.
4
(5 pts.)
(5 pts.)