Answer:
F(x=11)= (-31)
Step-by-step explanation:
for the function
F(x) = x² - 13*x + 22/x-11 , for x ≠ 11
then in order to define F(x=11) so F is continuous (see Note below) . By definition of continuity of a function:
F(x) is continuous in x=11 if lim F(x)=F(a) when x→a
then
when x→a , lim x² - 13x + 22/x-11 = lim 11² - 13*11 + 22/11 -11 = -3*11 + 2 = -31 = F(x=11)
then
F(x=11)= (-31)
Note:
F is not continuous in all x since
when x→0⁺ , lim (0⁺) ² - 13*0⁺ + 22/0⁺ -11 = (+∞)
when x→0⁻, lim (0⁻) ² - 13*0⁻ + 22/0⁻ -11 = (-∞)
then
limit F(x) , when x→0 does not exist since the limit from the left and from the right do not converge → since the limit does not exist , the function is not continuous in x=0
