Question

do it fast with explaination

Answer 1

any function is continuous function at a point x = a only when ,
f( a- ) = f(a + ) = f(a )
here ,

f(x ) = x² -( A +2)x + A when x ≠ 2

lim (x → 2-) { x² -(A +2)x + A }
put x = 2 , we see no any format gain by this , give finite value ,
e.g
f(2-) = 4 -(A +2)2 + A = 4 - 2A - 4 + A = -A

again,
similarly,
lim( x → 2+) { x² -(A +2)x + A}

f(2+) = 4 -(A +2)2 + A = - A

so,

f(2-)= f (2+) = f(2)

-A = - A = 2

A = -2

Answer 2

Answer:

lim( x → 2+) { x² -(A +2)x + A}

f(2+) = 4 -(A +2)2 + A = - A

f(2-)= f (2+) = f(2)

A = -2