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

$-3$

$1$

$4$

DNE

검증된 단계별 안내

Step 1: Understand the problem. We are tasked with estimating the limit of f(x) as x approaches -2, using the graph provided. A limit exists if the function approaches the same value from both the left and the right sides of the given x-value.

Step 2: Analyze the graph near x = -2. Observe the behavior of the function as x approaches -2 from the left (x → -2⁻) and from the right (x → -2⁺).

Step 3: From the graph, note that as x approaches -2 from the left, the function appears to approach a value near y = 5. However, as x approaches -2 from the right, the function appears to approach a value near y = 1.

Step 4: Since the function approaches different values (y = 5 from the left and y = 1 from the right), the limit does not exist. This is because the left-hand limit and the right-hand limit are not equal.

Step 5: Conclude that the limit of f(x) as x approaches -2 does not exist (DNE).

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).

$$\lim$_{x$\rightarrow$0^{-}}f$\left$(x$\right$)$ , $$\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$1}f$\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$0}f$\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$0}-4x+2$

Find the limit by creating a table of values.

$$\lim$_{x$\rarr$2}3x^2+5x+1$

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→−2f(x)\(\lim\)_{x\(\rarr\)-2}f\(\left\)(x\(\right\))limx→−2f(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\(\rarr\)-2}f\(\left\)(x\(\right\))$