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Let f:RtoR be a differentiable function ...

Let `f:RtoR` be a differentiable function having `f(2)=6,f'(2)=1/48` . Then evaluate `lim_(x to2)int_(6)^(f(x))(4t^(3))/(x-2)dt`.

Text Solution

Verified by Experts

The correct Answer is:
`16-f(4)`
`L=lim_(xto4)int_(4)^(x)((4t-f(t)))/((x-4))dt=limt_(xto4)(int_(4)^(1)(4t-f(t))dt)/(x-4)`
( `0//0` form , using L Hopital's rule)
`=lim_(xto 4)(4x-f(x))/1`
`16-f(4)`
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