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Find the first three terms in the expansion of

\sqrt{x^{2} + 4}

and give the range of values of $x$ for which this expansion is valid.

{(4 + x^{2})}^{\frac{1}{2}}

and factor out the $4.$

The binomial expansion will still work if you have $\frac{x^{2}}{4}$ in place of $x$ in the formula.

The expansion is valid when

| \frac{x^{2}}{4} | < 1

This is a quadratic inequality, so sketch a parabola to solve it.