Question

What is the limit as x is approaching 0 of the absolute value of x

Answer 1

The restriction of the outright worth of x as x methodologies 0 will be 0. Outright worth guarantees that the result is non-negative, and as x methodologies zero from one or the other side, the outcome stays at 0.

Step-by-step explanation:

The inquiry you're posing relates to the furthest reaches of the outright worth capability as the variable x methodologies are the worth of nothing. In science, explicitly in math, we assess cutoff points to comprehend the way of behaving of capabilities as they approach a specific point.

To track down the breaking point as x methodologies 0 of the outright worth of x, signified as lim x→0 |x|, we want to think about the meaning of outright worth. The outright worth of a number is the non-negative worth of that number regardless of its sign. In this manner, as x methodologies 0 from either the positive or negative side, the outright worth of x will likewise move toward 0.

Consequently, the cutoff is 0, since as x gets increasingly close to nothing, so does the outright worth of x.

Answer 2

recall that, an absolute value expression is a piece-wise in effect, thus we'd check the single-sided limits,


`\bf \lim\limits_(x\to 0)~|x|\implies \begin{cases} \lim\limits_(x\to 0^-)~-x\\\\ \lim\limits_(x\to 0^+)~+x \end{cases}\implies \begin{cases} 0\\\\ 0 \end{cases}\implies \lim\limits_(x\to 0)~|x|=0`