1. Limits and Continuity

Introduction to Limits

1. Limits and Continuity

Introduction to Limits

Business Calculus 때문에 힘들어하고 계신가요?

저희를 신뢰하는 수천 명의 학생들이 시험 합류하세요!

객관식

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

검증된 단계별 안내

Step 1: Observe the graph of f(x) and identify the behavior of the function as x approaches 1 from both the left and the right.

Step 2: From the graph, note that as x approaches 1 from the left (x → 1⁻), the value of f(x) is approaching 2.

Step 3: Similarly, as x approaches 1 from the right (x → 1⁺), the value of f(x) is also approaching 2.

Step 4: Since the left-hand limit and the right-hand limit are equal, the overall limit exists and is equal to the value that f(x) approaches, which is 2.

Step 5: Conclude that lim_{x→1}f(x) = 2 based on the consistent behavior of the function from both sides of x = 1.

3:33m

다음 시청

마스터 Cases Where Limits Do Not Exist Example 2가 Callie Rethman 짧은 영상으로 설명해 줍니다

관련 실천

객관식

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$)$

Find the limit by creating a table of values.

$$\lim$_{x$\rarr$0}-4x+2$

Introduction to Limits 연습 세트

수석 튜터가 만든 문제 세트

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