The function f is given by the formula f(x)=            2x^3−5x^2+12x−20         ----------------------                     x−2 when x<2 and by the formula ...

The function f is given by the formula

f(x)= 
          2x^3−5x^2+12x−20
        ---------------------- 
                   x−2

when x<2 and by the formula 

f(x)=5x^2−1x+a

when 2≤x. 


What value must be chosen for a in order to make this function continuous at 2?

Asked on by xfaceless

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Top Answer

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aruv | High School Teacher | (Level 2) Valedictorian

Posted on

`2x^3-5x^2+12x-20=2x^3-4x^2-x^2+2x+10x-20`

`=(x-2)(2x^2-x+10)`

`lim_(x->2-)f(x)=lim_(x->2-){(2x^3-5x^2+12x-20)/(x-2)}`

`=lim_(x->2-)(2x^2-x+10)=8-2+10=16`

and

`f(2)=5xx2^2-2+a=20-2+a=18+a`

function f will continous at x=2 if

`lim_(x->2)f(x)=f(2)`

`=> 18+a=16`

`a=16-18`

`a=-2`

The value of  a =-2 in order to make  function f(x) continuous at x= 2 .

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