Consider the piecewise function, $ f(x)=\{\table \;{x-|x|}/{x} , , \;\text " when "\; x < 0 ; 5 x^{2}+a , , \;\text " when "\; 0 ≤ x ≤ 1 ; b(\;{x^{2}-1}/{x^{2}-3 x+2}), , \;\text " when "\; 1 The function is continuous at x=0 and x=3 LHL at x=0 is equal to RHL at x=0
lim
x→0−
f(x)‌‌=
lim
x→0+
f(x)
lim
x→0−
‌
x−|x|
x
‌‌=
lim
x→0+
5x2+a
lim
x→0−
‌
x−(−x)
x
‌‌=
lim
x→0+
5x2+a
lim
x→0−
‌
2x
x
‌‌=
lim
x→0+
5x2+a
Solve further 2=a a=2 The function is continuous at x=3 LHL at x=3 is equal to RHL at x=3