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qtbabe9876a9

qtbabe9876a9

Answered question

2022-05-22

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

Answer & Explanation

Mihevcekd

Mihevcekd

Beginner2022-05-23Added 7 answers

Step 1
The distance between two points P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ) is given as ( x 1 - x 2 ) 2 + ( y 1 - y 2 ) 2
Step 2
with f ( t ) = ( ln ( t ) - e t , t 2 e t ) we get
f ( 2 ) = ( ln ( 2 ) - e 2 , 4 e 2 )
f ( 4 ) = ( ln ( 4 ) - e 4 , 16 e 4 )
so the distance is given by ( e 4 - e 2 - ln ( 2 ) ) 2 + ( 4 e 2 - 16 e 4 ) 2

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