Solution to calculus, assignment help

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gjraglavarunvef

Mathematics

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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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topen L 2. WA M her 2 curves Score Bees மோகனாங்க The questions refer to this TR picture. Z= fx)= 16 mxenya Hw ( We know if = (-2,-4 3 Test We para meterize C, and ca as follows, Gori(E)=
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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 ...


Anonymous
Really helped me to better understand my coursework. Super recommended.

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