Evaluate the following limits in Exercises 1 to 22: lim ₓ→₀ (sin ax)/bx

Solution:

At x = 0, the value of the given function takes the form 0/0, which is an indeterminate form.

So we will evaluate the given limit differently.

Now,

lim ₓ→₀ (sin ax)/bx

= lim ₓ→₀ ((sin ax)/ax) × (ax/bx) (multiplied and divided by ax)

= lim ₓ→₀ ((sin ax)/ax) × (a/b)

= a/b lim ₐₓ→₀ ((sin ax)/ax) [x → 0 ⇒ ax → 0]

= (a/b) × 1 [∵ lim_y→0 (siny/y) = 1]

= a/b

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 13

Evaluate the following limits in Exercises 1 to 22: lim ₓ→₀ (sin ax)/bx

Summary:

The value of the limit lim ₓ→₀ (sin ax)/bx is a/b