Question

Evaluate
$\rm \displaystyle \lim_{x\to 0}\ \frac{(1+x)^{6}-1}{(1+x)^{2}-1}$

Answer 1

Solution :

Given ,

$\rm \displaystyle \lim_{x\to 0}\ \frac{(1+x)^{6}-1}{(1+x)^{2}-1}$

If x -> 0 then ( x + 1 ) tends to 1

Now ,

= $\rm \displaystyle \lim_{(1+x)\to 1}\ \frac{(1+x)^{6}-1}{(1+x)^{2}-1}$

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We know that,

$\rm \displaystyle \lim_{x\to a}\ \frac{x^{m}-a^{m}}{x^{n}-a^{n}}$

= (m/n) × $a^{(m-n)}$

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= (6/2) × $1^{(6-2)}$

= 3 × 1

= 3

Therefore ,

$\rm \displaystyle \lim_{x\to 0}\ \frac{(1+x)^{6}-1}{(1+x)^{2}-1}$

= 3

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