What is the instantaneous velocity of an object moving in accordance to # f(t)= (e^(t-t^2),e^t/t^2) # at # t=2 #?

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Answer 1 · 2018-04-21T07:30:01

#(-3e^-2,0)#

velocity is #vec v#

#vec v = ((dx)/(dt),(dy)/(dt)) =(f'(t),g'(t))#

# #
# #
so, we need to know #f'(2)#

(1) #(e^(t-t^2))'=e^{t-t^2}(1-2t)#

(2) #(e^t/t^2)' = ((e^t*t^2)-(e^t*2t))/t^4#
# #
- TIP) #(f/g)'=(f'*g-f*g')/g^2#
# #
- TIP) #(e^t)'=e^t#
# #
# #

each (1), (2) input # t=2#

# #
1-1) #e^(2-4)xx(1-4)=##-3e^-2#,

2-1) #((e^2*4)-(e^2*4))/16=0#

# #
# #
#:. vec v = (-3e^-2,0)#