1. Limits and Continuity

Introduction to Limits

1. Limits and Continuity

Introduction to Limits

Difficoltà con Calculus?

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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$1}f$\left$(x$\right$)$

$0$

$1$

$2$

$DNE$

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Observe the graph of f(x) and identify the behavior of the function as x approaches 1 from both sides.

Notice that as x approaches 1 from the left (x < 1), the function f(x) is approaching the value 2.

Similarly, as x approaches 1 from the right (x > 1), the function f(x) is also approaching the value 2.

Since the function approaches the same value from both sides, the limit exists.

Conclude that the limit of f(x) as x approaches 1 is 2, because the function approaches the same value from both sides.

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Padroneggia Cases Where Limits Do Not Exist Example 2 con una breve spiegazione video di Nick Kaneko

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Using the graph, find the specified limit or state that the limit does not exist (DNE).

$\lim_{x \to - 2^{-}} f (x)$ , $\lim_{x \to - 2^{+}} f (x)$ , $\lim_{x \to - 2^{}} f (x)$

Using the graph, find the specified limit or state that the limit does not exist (DNE).

$$\lim$_{x$\rightarrow$0^{-}}f$\left$(x$\right$)$ , $$\lim$_{x$\rightarrow$0^{+}}f$\left$(x$\right$)$ , $$\lim$_{x$\rightarrow$0}f$\left$(x$\right$)$

Using the graph, find the specified limit or state that the limit does not exist.

$$\lim$_{x$\rightarrow$4^{-}}f$\left$(x$\right$)$ , $$\lim$_{x$\rightarrow$4^{+}}f$\left$(x$\right$)$ , $$\lim$_{x$\rightarrow$4}f$\left$(x$\right$)$

Find the specified limit or state that the limit does not exist by creating a table of values.

$f$\left$(x$\right$)=$\frac{1}{x}$$

$$\lim$_{x$\rightarrow$1^{-}}f$\left$(x$\right$)$ , $$\lim$_{x$\rightarrow$1^{+}}f$\left$(x$\right$)$ , $$\lim$_{x$\rightarrow$1}f$\left$(x$\right$)$

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$-2}f$\left$(x$\right$)$

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$)$

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$)$

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Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

f(−1)

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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→1f(x)\(\lim\)_{x\(\rarr\)1}f\(\left\)(x\(\right\))limx→1f(x)

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Set di pratica su Introduction to Limits

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\(\rarr\)1}f\(\left\)(x\(\right\))$