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For #f(t)= (sqrt(t+2)/(t+1),t^2+3t)# what is the distance between #f(0)# and #f(2)#?

Answer 1

Charles Anctil

The distance between #f(0)# and #f(2)# is #10.028#.

The coordinates of point for #f(0)# is #(sqrt(0+2)/(0+1),0^2+3xx0)# or #(sqrt2,0)#

and for #f(2)# we have #(sqrt(2+2)/(2+1),2^2+3xx2)# or #(2/3,10)#

The distance between the two points is

#sqrt((sqrt2-2/3)^2+(0-10)^2)=sqrt(0.74755^2+100)=10.028#

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Answer 2

Axel Alvarez

The distance between f(0) and f(2) for the function f(t) = (sqrt(t+2)/(t+1), t^2 + 3t) is sqrt(10)/3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.