Determine \begin{equation}\lim_{x\to 0}\,\frac{x^2(1+x)}{2x}.\end{equation}

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Lesson Parent: 
Function Limits V: Properties of Function Limits
Problem: 

Determine \begin{equation}\lim_{x\to 0}\,\frac{x^2(1+x)}{2x}.\end{equation}

Answer: 

0

SAMPLE SOLUTION

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Solution: 

This is the limit of the quotient of two polynomials. Since the denominator is zero the function is undefined at this point. Recall that we never actually get to $x=0$ because we restrict $x$ to <Sign in to see all the formulas> in the proof of

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In this particular problem, $a=0$ and therefore we are never actually at $x=0$. Because of this we can do the division by $x$ and rewrite the function as

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to see that

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We know that

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and therefore

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