Limit of \( \displaystyle \frac{\left(x + 1\right)^{2} - 1}{x} \) as \( x \to 0 \)

Problem 1.454 · easy

1. \[ \lim_{x \to 0^+}\left(\frac{\left(x + 1\right)^{2} - 1}{x}\right) \]
   limitStart with the limit of the given function.✓ Proved
2. \[ = \lim_{x \to 0^+}\left(\frac{x^{2} + 2 x}{x}\right) \]
   algebra simplifyExpand the numerator. Simplify the numerator by subtracting the constants.✓ Proved
3. \[ = \lim_{x \to 0^+}\left(x + 2\right) \]
   factor cancelFactor out x from the numerator. Cancel the common factor of x in the numerator and denominator.✓ Proved
4. \[ = 2 \]
   limitEvaluate the limit as x approaches 0.✓ Proved