Find limₓ→₀ f (x) and limₓ→₁ f (x), where f(x) = {2x + 3, x ≤ 0 and 3(x + 1), x > 0}

Solution:

The given function is f (x) = {2x + 3, x ≤ 0 and 3(x + 1), x > 0}

Now, we will evaluate the limits.

limₓ→₀₋ f (x) = limₓ→₀ [2x + 3] (as x < 0)

= 2 (0) + 3

= 3

limₓ→₀₊ f (x) = limₓ→₀ 3(x + 1) (as x > 1)

= 3(0 + 1)

= 3

Hence,

limₓ→₀₋ f (x) = limₓ→₀₊ f (x) = 3

So  limₓ→₀ f (x) = 3

Now,

limₓ→₁ f (x) = limₓ→₁ 3 (x + 1) (as 1 > 0)

= 3(1 + 1)

= 6

Hence,

limₓ→₀ f (x) = 3 and limₓ→₁ f (x) = 6

---

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 23

Find limₓ→₀ f (x) and limₓ→₁ f (x), where f(x) = {2x + 3, x ≤ 0 and 3(x + 1), x > 0}

Summary:

We found that limₓ→₀ f (x) = 3 and limₓ→₁ f (x) = 6