The energy of a system is given as E ( t )= ^3 e ^ - t , where t is the time and =0.3 ~s ⁻¹ . The errors in the measurement of and t are 1.2 % and 1.6 % , respectively. At t=5 ~s , maximum percentage error in the energy is :

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Correct answer: A. 6 %

aligned & d E=3 ^2 d e^ - t + ^3 e^ - t (- ) d t & d E E = 3 d +(- ) d t & E E = 3 + t aligned ( %) t=1.6 % 5=8 % % ( 3 )=3 1.2 %=3.6 % Putting values we get 3.6+8 0.3=6 %

The energy of a system is given as E ( t )= ^3 e ^ - t , where t is the time and =0.3 ~s ⁻¹ . The errors in the measurement of and t are 1.2 % and 1.6 % , respectively. At t=5 ~s , maximum percentage error in the energy is :

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