[Solved] Evaluate the given limit: x→0limx(x+1)5−1 - Mathematics

limx→0x(x+1)5−1 Put x + 1 = y so that y → 1 as x→0 Accordingly, limx→0x(x+1)5−1=limy→1y−1y5−1 =limy→1y−1y5−13 =5.15−1[limx→ax−axn−an=nan−1] =5

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Evaluate the given limit: _{x 0}{ ( x+1 )^{5}-1}{x}

Mathematics

Class 11

NCERT

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Chapter 13: Limits and Derivatives

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Evaluate the Given limit: lim_{x \to - 1} \frac{x ^{10} + x ^{5} + 1}{x - 1}

Evaluate the given limit:

x \to 0 lim \frac{( x + 1 ) ^{5} - 1}{x}

Evaluate the Given limit:

x \to 2 lim \frac{3 x ^{2} - x - 10}{x ^{2} - 4}

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Question

Easy

Solving time: 1 mins

Evaluate the given limit: $x \to 0 lim \frac{( x + 1 ) ^{5} - 1}{x}$

Views: 6,121 students

Book:

Mathematics (NCERT)

Text solutionVerified

lim_{x \to 0} \frac{( x + 1 ) ^{5} - 1}{x}

Put x + 1 = y so that y

\to

1 as

x \to 0

Accordingly,

lim_{x \to 0} \frac{( x + 1 ) ^{5} - 1}{x} = lim_{y \to 1} \frac{y ^{5} - 1}{y - 1}

= lim_{y \to 1} \frac{y ^{5} - 1 ^{3}}{y - 1}

= 5. 1^{5 - 1} [lim_{x \to a} \frac{x ^{n} - a ^{n}}{x - a} = n a^{n - 1}]

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Evaluate the Given limit: lim_{x \to - 1} \frac{x ^{10} + x ^{5} + 1}{x - 1}

Evaluate the given limit:

x \to 0 lim \frac{( x + 1 ) ^{5} - 1}{x}

Evaluate the Given limit:

x \to 2 lim \frac{3 x ^{2} - x - 10}{x ^{2} - 4}

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Question Text	Evaluate the given limit: $x \to 0 lim \frac{( x + 1 ) ^{5} - 1}{x}$
Topic	Limits and Derivatives
Subject	Mathematics
Class	Class 11
Answer Type	Text solution:1
Upvotes	37

Evaluate the given limit: $x \to 0 lim \frac{( x + 1 ) ^{5} - 1}{x}$

Text solutionVerified

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