f(x) = 4 sin2 x + 3 cos2 x की सीमा क्या है?

  1. [3, 4]
  2. (3, 4)
  3. (4, 7)
  4. (0, 3]

Answer (Detailed Solution Below)

Option 1 : [3, 4]
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Detailed Solution

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धारणा:

-1 ≤ sin x ≤ 1

0 ≤ sin2 x ≤ 1

गणना:

दिया हुआ:

f(x) = 4 sin2 x + 3 cos2 x

= sin2 x + 3 sin2 x + 3 cos2 x

= sin2 x + 3 (sin2 x + cos2 x)

= sin2 x + 3               (∵sin2 x + cos2 x = 1)

जैसा कि हम जानते हैं कि, 0 ≤ sin2 x ≤ 1

⇒ 3 + 0 ≤ 3 + sin2 x ≤ 3 + 1

⇒ 3 ≤ f(x) ≤ 4

∴ f(x) की सीमा [3, 4] है

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