Ex 13.1, 8 - Evaluate limit lim x->3 (x4 - 81/2x2-5x-3) - Ex 13.1

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  1. Chapter 13 Class 11 Limits and Derivatives
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Ex 13.1, 8 Evaluate the Given limit: lim﷮x→3﷯ x4 −81﷮2x2 −5x−3﷯ lim﷮x→3﷯ x4 − 81﷮2x2 − 5x − 3﷯ = 3﷯4 − 81﷮2 3﷯2 − 5 3﷯ − 3﷯ = 81 − 81﷮18 − 15 − 3﷯ = 0﷮0﷯ Since it is a 0﷮0﷯ form we simplify as lim﷮x→3﷯ x4 − 81﷮2x2 − 5x − 3﷯ = lim﷮x→3﷯ (𝑥2)﷮2﷯− (9)﷮2﷯﷮2x2 −6x + x − 3﷯ lim﷮x→3﷯ x4 − 81﷮2x2 − 5x − 3﷯ = lim﷮x→3﷯ (𝑥2)﷮2﷯− (9)﷮2﷯﷮2x2 −6x + x − 3﷯ = lim﷮x→3﷯ x2 − 9﷯ (x2 + 9)﷮2x x − 3﷯ + 1 (x − 3)﷯ = lim﷮x→3﷯ 𝑥2− 3﷯2﷯(𝑥2 + 9)﷮ x + 1﷯(𝑥 − 3)﷯ = lim﷮x→3﷯ 𝑥 − 3 ﷯ ( 𝑥 + 3)(𝑥2 + 9)﷮ 2𝑥 + 1﷯ (𝑥 − 3)﷯ = 𝐥𝐢𝐦﷮𝐱→𝟑﷯ 𝒙 + 𝟑 ﷯ (𝒙𝟐 + 𝟗)﷮𝟐𝒙 + 𝟏﷯ = 3 + 3﷯( 3﷯2 + 9)﷮2 ×3 +1﷯ = 6 (9 + 9)﷮6 + 1﷯ = 6(18)﷮7﷯ = 𝟏𝟎𝟖﷮𝟕﷯

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