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Frank Day 2022-07-15 Answered
For f ( t ) = ( ( ln t ) 2 t , t 3 ) what is the distance between f(2) and f(4)?
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Answers (1)

Freddy Doyle
Answered 2022-07-16 Author has 20 answers
Step 1
We have a parametric function giving us cartesian coordinates for the specified parameter:
f ( t ) = ( ( ln t ) 2 t , t 3 )
This with t = 2 we get:
f ( 2 ) = ( ( ln 2 ) 2 2 , 8 )
And with t = 4 we get:
f ( 4 ) = ( ( ln 4 ) 2 4 , 64 )
= ( ( ln 2 2 ) 2 4 , 64 )
= ( ( 2 ln 2 ) 2 4 , 64 )
= ( ( ln 2 ) 2 , 64 )
Step 2
The distance. d, between these two cartesian coordinates is given by pythagoras:
d 2 = ( ( ln 2 ) 2 - ( ln 2 ) 2 2 ) 2 + ( 64 - 8 ) 2
= ( ( ln 2 ) 2 2 ) 2 + ( 56 ) 2
= ( ln 2 ) 4 4 + 3136
Giving: d = ( ln 2 ) 4 4 + 3136
    56.000515 ...

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