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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

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

<Sign in to see all the formulas>

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

<Sign in to see all the formulas>

to see that

<Sign in to see all the formulas>

We know that

<Sign in to see all the formulas>

and therefore

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