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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Evaluate the following : limx→0[secx2-1x4]

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प्रश्न

Evaluate the following :

`lim_(x -> 0)[(secx^2 - 1)/x^4]`

बेरीज
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उत्तर

`lim_(x -> 0)(secx^2 - 1)/x^4`

Put x2 = y

As x → 0, x2 → 0

∴ y → 0

∴ Required limit

= `lim_(y -> 0) (sec y - 1)/(y^2)`

= `lim_(y -> 0) (sec y - 1)/(y^2) xx (sec y + 1)/(sec y + 1)`

= `lim_(y -> 0) (sec^2 y - 1)/(y^2(sec y + 1))`

= `lim_(y -> 0) (tan^2 y)/(y^2(sec y + 1))`

= `lim_(y -> 0) (tan^2 y)/(y^2) xx 1/(sec y + 1)`

= `lim_(y -> 0) ((tan^2 y)/y^2) xx lim_(y -> 0) 1/(sec y + 1)`

= `(1)^2 xx 1/(1 + 1)`

= `1/2`

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पाठ 7: Limits - Miscellaneous Exercise 7.2 [पृष्ठ १५९]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 7 Limits
Miscellaneous Exercise 7.2 | Q II. (7) | पृष्ठ १५९

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