Let S= ( , ) R R: f(t)= (| | e^t- ) (2|t|) . , t R , is a differentiable function . Then S is a subest of?

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Correct answer: A. R [0, )

aligned & S= ( , ) R R : f ( t )= (| | e ^ t - ) (2 t ), . &t R &f(t)= (| | e ^ |t| - ) (2|t|) & array l (| | e^t- ) 2 t t>0 (| | e^ -t - )(- 2 t) t 0 | | e ^ -t 2 t+ (| | e^ -t - )(-2 2 t) < t < 0 array . & As, f(t) is differentiable & LHD = RHD at t=0 &| | 2(0)+ (| | e ^0- ) 2 (0) &=| | e ⁻⁰ 2(0)-2 (0) (| | e ⁻⁰- ) & 0+(| |- ) 2=0-2(| |- ) & 4(| |- )=0 & | |= aligned So, S ( , )= R & [0, ) Therefore set S is subset of R [0, )

Let S= ( , ) R R: f(t)= (| | e^t- ) (2|t|) . , t R , is a differentiable function . Then S is a subest of?

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