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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 6 of 72
Marks: +1, -0
lim⁡x→0(x+1)5−1x\lim\limits_{x\to 0}\frac{(x+1)^5-1}{x}
Solution:  
We have, lim⁡x→0(x+1)5−1x\lim\limits_{x\to 0}\frac{(x+1)^5-1}{x} (0/0 form)
Put y = 1 + x, so that y → 1 as x → 0
Then lim⁡x→0(x+1)5−1x\lim\limits_{x\to 0}\frac{(x+1)^5-1}{x} = lim⁡y→1y5−1y−1\lim\limits_{y\to 1}\frac{y^5-1}{y-1} = 5(1)5−15(1)^{5-1} = 5.
[Using lim⁡x→axn−anx−a\lim\limits_{x\to a}\frac{x^n-a^n}{x-a} = n(a)n−1n(a)^{n-1}]
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