Question

Find the value of 'k' if the function

`f(X)=(tan7x)/(2x) ,  "for " x != 0 `

`=k`,            for x=0

is continuos at x=0

Answer 1

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`