Lim_x → 0(a+x)^2 a^2/x =lim_x → 0(a+x a)(a+x+a)/x =lim_x → 0(x)(2a+x)/x =lim_x → 0 (2a+x)=2a ...

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Expansions to Remove Indeterminate Form

lim x → 0a+x2...

Question

${lim}_{x \to 0} \frac{(a + x)^{2} - a^{2}}{x}$

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Solution

${lim}_{x \to 0} \frac{(a + x)^{2} - a^{2}}{x}$

$= {lim}_{x \to 0} \frac{(a + x - a) (a + x + a)}{x}$

$= {lim}_{x \to 0} \frac{(x) (2 a + x)}{x}$

$= {lim}_{x \to 0} (2 a + x) = 2 a$

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