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Evaluate the following limits: limx→∞1+x-3x31+x2+3x3 - Mathematics

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प्रश्न

Evaluate the following limits:

`lim_(x -> oo) (1 + x - 3x^3)/(1 + x^2 +3x^3)`

बेरीज
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उत्तर

`lim_(x -> oo) (1 + x - 3x^3)/(1 + x^2 +3x^3) = lim_(x - oo) (x^3(1/x^3 + x/x^3 - 3))/(x^3 (1/x^3 + x^2/x^3 + 3))`

= `lim_(x -> oo) ((1/x^3 + 1/x^2 - 3)/(1/x^3 + 1/x + 3))`

= `((1/oo + 1/oo - 3)/(1/oo + 1/oo + 3))`

= `(0 + 0 - 3)/(0 + 0 + 3)`

= `(-3)/3`

`lim_(x -> oo) (1 + x - 3x^3)/(1 + x^2 +3x^3)` = – 1

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पाठ 9: Differential Calculus - Limits and Continuity - Exercise 9.3 [पृष्ठ १११]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 9 Differential Calculus - Limits and Continuity
Exercise 9.3 | Q 6 | पृष्ठ १११

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