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Ex 13.1, 7 - Evaluate lim x->2 3x2 - x - 10 / x2 - 4 - Limits - 0/0 form

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  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise
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Ex 13.1, 7 Evaluate the Given limit: lim﷮x→2﷯ 3x2 −x−10﷮x2 −4﷯ lim﷮x→2﷯ 3x2 − x − 10﷮x2 − 4﷯ = 3 × 2﷮2﷯ − 2 −10﷮ 2﷮2﷯ − 4﷯ = 3 × 4 − 2 −10﷮4 − 4﷯ = 12 − 12﷮4 − 4﷯ = 0﷮0﷯ Since it is of form 0﷮0﷯, we simplify as lim﷮x→2﷯ 3x2 − x − 10﷮x2 − 4﷯ = lim﷮x→2﷯ 3x2+ 5x − 6x − 10﷮x2 − 4﷯ lim﷮x→2﷯ 3x2 − x − 10﷮x2 − 4﷯ = lim﷮x→2﷯ 3x2+ 5x − 6x − 10﷮x2 − 4﷯ = lim﷮x→2﷯ x 3x + 5﷯ − 2 (3x + 5)﷮x2 − 2﷮2﷯﷯ = lim﷮x→2﷯ 𝑥 − 2﷯(3𝑥 + 5)﷮ x − 2﷯(𝑥 + 2)﷯ = 𝐥𝐢𝐦﷮𝐱→𝟐﷯ 𝟑𝒙 + 𝟓﷮𝒙 + 𝟐﷯ = 3 × 2 + 5﷮2 + 2 ﷯ = 6 + 5﷮4﷯ = 𝟏𝟏﷮𝟒﷯

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