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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.)

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