If

is continuous at then find the values of a and b.

Given f(x) is continuous at x = 0

At x = 0 f(x) = 2

We know if a function is continuous then

Left hand limit = Right hand limit = f(k), where k is const.

Left-hand limit

⇒

By l’hospital rule,

⇒

X = 0

Left hand limit = - (a + 1) + 2

Right hand limit

⇒

By l’hospital rule,

⇒

X = 0

Right hand limit = b/2

We know if a function is continuous then

Left hand limit = Right hand limit = f(k), where k is const.

∴ - (a + 1) + 2 = 2

a = 1

∴ b/2 = 2

⇒ b = 4.