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What is the instantaneous velocity of an object with position at time t equal to # f(t)= (te^(t^2-3t),t^2-e^t) # at # t=3 #?

1 Answer

Jun 24, 2016

#(10, 6 - e^3) #

Explanation:

#f(t)= (te^(t^2-3t),t^2-e^t)#
#f'(t)= (e^(t^2-3t) + t (2t-3) e^(t^2-3t),2t-e^t)#
#= (e^(t^2-3t) (1 + t (2t-3)),2t-e^t)#

#f'(3) = ( (1)(1 + 3(3)), 6 - e^3) = (10, 6 - e^3) #

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