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  4. The value of displaystyle limx → 0 (|3x2 + 1|/2x2 + 1) is :

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Q. The value of $\displaystyle\lim_{x \to 0} \frac{|3x^2 + 1|}{2x^2 + 1}$ is :

Limits and Derivatives

Solution:

Consider $\displaystyle\lim_{x \to 0} \frac{|3x^2 + 1|}{2x^2 + 1}$
$= \displaystyle\lim_{x\to0} \frac{3x^{2} +1}{2x^{2} +1} = \displaystyle\lim _{x\to 0} \frac{x^{2}\left(3 + \frac{1}{x^{2}}\right)}{x^{2} \left(2+ \frac{1}{x^{2}}\right)}$
$ =\displaystyle\lim _{x\to 0} \frac{3+1 /x^{2}}{2+1 /x^{2}} = \frac{3+0}{2+0} =\frac{3}{2}$