Use the graph of $f$\left$(x$\right$)$ to estimate the value of the limit or state that it does not exist (DNE).
$$\lim$_{x$\rarr$0}f$\left$(x$\right$)$

$0$

$1$

$5$

DNE

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Step 1: Understand the problem. We are tasked with estimating the value of the limit $ \lim_{x \to 0} f(x) $ using the graph of $ f(x) $. The limit represents the behavior of the function $ f(x) $ as $ x $ approaches 0 from both the left and the right.

Step 2: Analyze the graph near $ x = 0 $. Observe the behavior of the function $ f(x) $ as $ x $ approaches 0 from the left (negative side) and from the right (positive side).

Step 3: From the graph, note that as $ x \to 0^- $ (approaching 0 from the left), the function $ f(x) $ increases without bound, heading towards positive infinity. Similarly, as $ x \to 0^+ $ (approaching 0 from the right), $ f(x) $ also increases without bound, heading towards positive infinity.

Step 4: Recall the definition of a limit. For the limit $ \lim_{x \to 0} f(x) $ to exist, the function must approach a single finite value from both sides as $ x \to 0 $. In this case, $ f(x) $ does not approach a finite value; instead, it diverges to infinity.

Step 5: Conclude that the limit $ \lim_{x \to 0} f(x) $ does not exist (DNE) because the function diverges to infinity as $ x \to 0 $.

3:33m

다음 시청

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전문가 영상 설명

Business Calculus 때문에 힘들어하고 계신가요?

Use the graph of f(x)f\(\left\)(x\(\right\))f(x)to estimate the value of the limit or state that it does not exist (DNE).limx→0f(x)\(\lim\)_{x\(\rarr\)0}f\(\left\)(x\(\right\))limx→0f(x)

다음 시청

Introduction to Limits 연습 세트

Use the graph of $f\(\left\)(x\(\right\))$ to estimate the value of the limit or state that it does not exist (DNE).
$\(\lim\)_{x\(\rarr\)0}f\(\left\)(x\(\right\))$