Description
I'm trying to dig myself out of a hole for this assignment.
I worked out problem #1, and think I've got problem #3 by proxy. Please make those a lower priority, but I would appreciate an explanation of those as well.
For question II (question #2), is the symbol given referring to the tangent of the companion curve with the x,y curve? How do I solve question #2?
If somebody can give me intellegent answers for the majority of these questions within 20 hours, I would very much appreciate it.
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Explanation & Answer
here's my solution
PART I:
The point 1,1, 2 on the surface z f x, y 6 x 2 y 2 is projected onto the point 1,1 on the xyplane. The curve C1 : r1 t t , t 3 passes through this point at t 1.
Thus, the unit vector T1 tangent to the curve C1 is calculated by
T1 t
1,3t
r1 t
r1 t
1 9t 2
1
1 9t 2
,
3t
1 9t 2
At t 1, we have
1
T1 1
1 9t 2
,
3t
1 9t 2
Hence, the directional derivative
df
f T1
ds
x y
,
z z
1
3
,
10 10
1 1
,
2 2
1
3
,
10 10
1
1 9 1
2
,
3 1
1 9 1
2
1
3
,
10 10
df
taken at 1,1, 2 in the direction of T1 is calculated by
du
1 1
1 3
2 10 2 10
2
10
PART II:
Since ...
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