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Ex 13.1, 6 - Evaluate: lim x->0  (x + 1)5 -1/x - Class 11 - Limits - 0/0 form

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  1. Class 11
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Ex 13.1, 6 Evaluate the Given limit: lim﷮x→0﷯ x +1﷯5 −1﷮x﷯ lim﷮x→0﷯ x + 1﷯5 − 1﷮x﷯ = 0 + 1﷯5 −1﷮0﷯ = 15 − 1﷮0﷯ = 1 − 1﷮0﷯ = 0﷮0﷯ Since it is of from 0﷮0﷯ Hence, we simplify lim﷮x→0﷯ x +1﷯5 −1﷮x﷯ Putting y = x + 1 ⇒ x = y – 1 As x → 0 y → 0 + 1 y → 1 Our equation becomes lim﷮x→0﷯ x +1﷯5 −1﷮x﷯ = lim﷮y→1﷯ 𝑦5 − 1﷮y − 1﷯ = 𝐥𝐢𝐦﷮𝐲→𝟏﷯ 𝒚𝟓 − 𝟏﷮𝟓﷯﷮𝐲 − 𝟏﷯

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