A function f(x) is said to be continuous at x = c if,

Left hand limit (LHL at x = c) = Right hand limit(RHL at x = c) = f(c).

Mathematically we can represent it as-

Where h is a very small number very close to 0 (h→0)

Now according to above theory-

f(x) = x³ + 2x – 1 is continuous at x = 1 if -

Clearly,

LHL =

∴ LHL = (1-0)³ + 2(1-0) – 1 = 2 …(1)

Similarly, we proceed for RHL-

RHL =

∴ RHL = (1+0)³ + 2(1+0) – 1 = 2 …(2)

And,

f(1) = (1+0)³ + 2(1+0) – 1 = 2 …(3)

Clearly from equation 1 , 2 and 3 we can say that

∴ f(x) is continuous at x = 1