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gnatopoditw

gnatopoditw

Answered question

2022-06-22

For f ( t ) = ( ln t t , t 2 e t ) what is the distance between f(2) and f(4)?

Answer & Explanation

Raven Higgins

Raven Higgins

Beginner2022-06-23Added 17 answers

Step 1
We have: f ( t ) = ( ln t t , t 2 e t )
Put t = 2 :
f ( 2 ) = ( ln 2 2 , 4 e 2 )
Put t = 4
f ( 4 ) = ( ln 4 4 , 16 e 4 )
            = ( ln 2 2 4 , 16 e 4 )
            = ( 2 ln 2 4 , 16 e 4 )
            = ( ln 2 2 , 16 e 4 )
Step 2
By Pythagoras:
d 2 = Δ x 2 + Δ y 2
      = ( 0 ) 2 + ( 4 e 2 - 16 e 4 ) 2
d = 4 e 2 - 16 e 4
              = 4 ( e 2 - 4 ) e 4

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