suppose that ...

Question

suppose that limit as x->-2    f(x)-4/x-2=1/2. find limit as x->-2 f(x).

Answer 1

 

Is the equation  f(x) - 4/(x-2) ?  [ as written above, it looks like   f(x) - 4/x -2, which is very different ] 

 

 

Assuming it is  f(x) - 4/(x-2):

 

   Lim _{[x —> -2]} { f(x) - 4/(x-2) }  = 1/2    is given

 

So we just need to isolate Lim { f(x) } on one side:

 

   Lim _{[x —> -2 ]}  { f(x} } -  Lim _{[x —> -2]} { 4/(x - 2) } = 1/2

 

 

   Lim _{[x —> -2 ]} { f(x} } =   1/2 + Lim _{[x —> -2]} { 4/(x - 2) }   

 

                                    =  1/2 + (4/(-2-2))

                                    =  -1/2