Question
Download Solution PDFf(x) = 4 sin2 x + 3 cos2 x की सीमा क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
-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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