# 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

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