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Evaluate the following limits: limx→01-x-1x2 - Mathematics

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प्रश्न

Evaluate the following limits:

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

बेरीज
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उत्तर

`lim_(x -> 0) (sqrt(1 - x) - 1)/x^2 =  lim_(x -> 0) [(sqrt(1 - x) - 1)/x^2 xx (sqrt(1 - x) + 1)/(sqrt(1 - x) + 1)]`

= `lim_( -> 0) [((1 - x) - 1)/(x^2 (sqrt(1 - x) + 1))]`

= `lim_(x -> 0) [(- x)/(x(sqrt(1 - x) + 1))]`

= `- lim_(x -> 0) [1/(x(sqrt(1 - x) + 1))]`

= `- 1/(0(sqrt(1 - 0) + 1))`

= `- oo`

∴ `lim_(x -> 0) (sqrt(1 - x) - 1)/x^2` does not exist.

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Concept of Limits
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Calculus - Limits and Continuity - Exercise 9.2 [पृष्ठ १०३]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 9 Differential Calculus - Limits and Continuity
Exercise 9.2 | Q 13 | पृष्ठ १०३

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