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Evaluate the following limits in Exercises 1 to 22: lim ₓ→₀ (sin ax)/(sin bx), a, b ≠ 0
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, the given limit is
lim ₓ→₀ (sin ax)/(sin bx)
Multiplying and dividing by each of ax and bx,
= lim ₓ→₀ [ [ax/bx] (sin ax/ax)/lim ₓ→₀ [(sin bx/bx)]
When x → 0 ⇒ ax → 0 and x → 0 ⇒ bx → 0. So the above limit becomes
= (a/b) [lim ₐₓ→₀ (sin ax/ax)] / [lim bₓ→₀ (sin bx/bx) ]
= a/b × 1/1 [∵ limy→0 (siny/y) = 1]
= a/b
NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 14
Evaluate the following limits in Exercises 1 to 22: lim ₓ→₀ (sin ax)/(sin bx), a, b ≠ 0
Summary:
The value of the limit lim ₓ→₀ (sin ax)/(sin bx), a, b ≠ 0 is a/b
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