#### Question

Find the value of 'k' if the function

`f(X)=(tan7x)/(2x) , `

`=k`, for x=0

is continuos at x=0

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#### Solution

Given

`f(X)=(tan7x)/(2x) ,`

`=k`

f(0)=k

`Now lim_(x->0)f(x)= lim_(x->0)(tan7x)/(2x)`

` = lim_(x->0)(tan7x)/(7x)7/2`

` =1xx 7/2`

as function f(x) is coninuous at x=0

`lim_(x->0)f(x)=f(0)=k`

`k=7/2`

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