NTA CUET Mathematics With Fully Solved 2023 Papers by Pearson

CHAPTER 2

Limits Continuity and Differentiability

CHAPTER AT A GLANCE

Definition: Limit of a function f(x) is said to exist, as x → a when,

f (a − h) = f (a + h) = Finite

(Left hand limit) (Right hand limit)

Note that we are not interested in knowing about what happens at x = a. Also note that if L.H.L. and R.H.L. are both tending towards ‘ ∞’ or ‘−∞’, then it is said to be an infinite limit.

Remember, ‘x → a’ means that x is approaching to ‘a’ but not equal to ‘a’.

Fundamental Theorems on Limits

Let f (x) = and g (x) = m. If ℓ and