For #f(t)= (1/t,-1/t^2)# what is the distance between #f(2)# and #f(5)#?
1 Answer
Jan 2, 2016
Explanation:
Find the two points described by
#f(2)=(1/2,-1/(2^2))=(1/2,-1/4)#
#f(5)=(1/5,-1/5^2)=(1/5,-1/25)#
Use the distance formula to find the distance between the points.
#d=sqrt((1/2-1/5)^2+(-1/4-(-1/25))^2)#
#=sqrt((5/10-2/10)^2+(-25/100+4/100)^2)#
#=sqrt((3/10)^2+(-21/100)^2)#
#=sqrt(9/100+441/10000)#
#=sqrt((900+441)/10000#
#=sqrt1341/100=(3sqrt149)/100approx0.3662#
