Maharashtra State BoardHSC Commerce 11th
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Evaluate the following limits: limx→-3[x+3x2+4x+3] - Mathematics and Statistics

Sum

Evaluate the following limits: `lim_(x -> - 3)[(x + 3)/(x^2 + 4x + 3)]` 

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Solution

`lim_(x -> - 3)[(x + 3)/(x^2 + 4x + 3)]` 

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

= `lim_(x -> - 3) 1/(x + 1)    ...[("As"  x -> -3","  x ≠ - 3),(therefore x + 3 ≠ 0)]`

= `1/(-3 + 1)`

= `-1/2`

Concept: Factorization Method
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