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• RD Sharma Class 11 Solutions for Maths

# Class 11 RD Sharma Solutions – Chapter 29 Limits – Exercise 29.9

### Question 1. Solution:

Given, By Applying limits, we get, = (Indeterminate form or 0/0 form)

So, we cannot just directly apply the limits as we got indeterminate form.

On substituting we get,

⇒ We know, sin2x + cos2x = 1

⇒ sin2x = 1 – cos2

⇒ By using a2 b2 = (a + b)(a b) we get,

⇒ ⇒ Applying limits we get,

⇒ ⇒ Therefore, the value of ### Question 2. Solution:

Given, Applying the limits, we get,

⇒ (Indeterminate form)

So, we cannot just directly apply the limits as we got indeterminate form.

We know, cosec2x − cot2x = 1

⇒ cosec2x = 1 + cot2

⇒ ⇒ By using formula, a2 b2 = (a + b)(a b) we get,

⇒ ⇒ Applying the limits, we get,

⇒ Therefore, the value of ### Question 3. Solution:

Given, Applying the limits, we get,

⇒ (Indeterminate form)

We know, cosec2x − cot2x = 1 ⇒ cot2x = cosec2x – 1

⇒ ⇒ By using formula, a2 b2 = (a + b)(a b) we get,

⇒ ⇒ Applying the limits, we get,

⇒ Therefore, the value of ### Question 4. Solution:

Given, Applying the limits we get,

⇒ (Indeterminate form)

So, we cannot just apply the limits.

We know, cosec2x − cot2x = 1 ⇒ cosec2x = 1 – cot2 ⇒ By using formula, a2 b2 = (a + b)(a b) we get, ⇒ Applying the limits we get,

⇒ Therefore, The value of ### Question 5. Solution:

Given, Applying the limits, we get,

⇒ (Indeterminate form)

So, we cannot just apply the limits.

Rationalizing the numerator(multiplying and dividing with )

⇒ ⇒ Let x = π − h

If x π, h → 0

Substituting x = π − h we get, We know that cos(π x) = −cosx substituting we get,

⇒ By using cos2x = 1 − 2sin2x cos h = 1 − 2sin2(h​/2) ⇒ We know that, Applying the limits, we get,

⇒ ⇒ 1/2 x 1/2 = 1/4

Therefore, the value of ### Question 6. Solution:

Given, Applying the limits, we get,

⇒ (Indeterminate form)

So, we cannot just directly apply the limits,

By using the formula, a3 + b3 = (a + b)(a2 ab + b2) we get, By using formula, a2 b2 = (a + b)(a b)

⇒ ⇒ Applying the limits, we get,

⇒ Therefore, the value of My Personal Notes arrow_drop_up
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