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Evaluate the following limits in Exercises 1 to 22: limₓ→₀ (ax + x cos x)/(b sin x)
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,
limₓ→₀ (ax + x cos x)/(b sin x)
= 1/b limₓ→₀ x(a + cos x)/(sin x)
= 1/b limₓ→₀ x/(sin x) · limₓ→₀ (a + cos x)
= 1/b · 1/[limₓ→₀ (sin x/x)] · limₓ→₀ (a + cos x)
= 1/b · 1/1 · (a + cos 0) [∵ limₓ→₀ (sin x/x) = 1]
= (a + 1)/b
NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 18
Evaluate the following limits in Exercises 1 to 22: limₓ→₀ (ax + x cos x)/(b sin x)
Summary:
The value of the limit limₓ→₀ (ax + x cos x)/(b sin x) is (a + 1)/b
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