(A) limx →-2 f(x) (B) limx →-2^+ f(x) (C) limx →-2 f(x) (D) f(-2) (E) Is f continuous at x=-2 ?

Name: Problem 22, Chapter 2: Calculus for Business, Economics, Life Sciences, and Social Sciences
Uploaded: 2021-03-22T05:44:53-08:00
Duration: 1 min 3 s
Channel: Dwijendra Rao
Description: (A) limx →-2 f(x) (B) limx →-2^+ f(x) (C) limx →-2 f(x) (D) f(-2) (E) Is f continuous at x=-2 ? Explain.(A) limx →-1^- f(x) (B) limx →-1^+ f(x) (C) limx →-1 f(x) (D) f(-1) (E) Is f continuous at x=-1 ? Explain.

step 1 We have to find the limit exchange to minus 1 minus minus 1 minus so this is the point minus 1 a

Question

(A) $\lim _{x \rightarrow-2} f(x)$ (B) $\lim _{x \rightarrow-2^{+}} f(x)$ (C) $\lim _{x \rightarrow-2} f(x)$ (D) $f(-2)$ (E) Is $f$ continuous at $x=-2 ?$ Explain.(A) $\lim _{x \rightarrow-1^{-}} f(x)$ (B) $\lim _{x \rightarrow-1^{+}} f(x)$ (C) $\lim _{x \rightarrow-1} f(x)$ (D) $f(-1)$ (E) Is $f$ continuous at $x=-1 ?$ Explain.

   (A) $\lim _{x \rightarrow-2} f(x)$
(B) $\lim _{x \rightarrow-2^{+}} f(x)$
(C) $\lim _{x \rightarrow-2} f(x)$
(D) $f(-2)$
(E) Is $f$ continuous at $x=-2 ?$ Explain.(A) $\lim _{x \rightarrow-1^{-}} f(x)$
(B) $\lim _{x \rightarrow-1^{+}} f(x)$
(C) $\lim _{x \rightarrow-1} f(x)$
(D) $f(-1)$
(E) Is $f$ continuous at $x=-1 ?$ Explain.

Calculus for Business, Economics, Life Sciences, and Social Sciences

Raymond A. Barnett,… 13th Edition

Chapter 2, Problem 22

Instant Answer

Solved by Expert Dwijendra Rao

03/22/2021

Step 1

This is represented as $\lim _{x \rightarrow-2^{-}} f(x)$. Show more…

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(A) $\lim _{x \rightarrow-2} f(x)$ (B) $\lim _{x \rightarrow-2^{+}} f(x)$ (C) $\lim _{x \rightarrow-2} f(x)$ (D) $f(-2)$ (E) Is $f$ continuous at $x=-2 ?$ Explain.(A) $\lim _{x \rightarrow-1^{-}} f(x)$ (B) $\lim _{x \rightarrow-1^{+}} f(x)$ (C) $\lim _{x \rightarrow-1} f(x)$ (D) $f(-1)$ (E) Is $f$ continuous at $x=-1 ?$ Explain.

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Key Concepts

Continuity

Continuity at a point means that the function's value at that point matches the limit of the function as the input approaches that point from both sides. In other words, for continuity, the left-hand and right-hand limits must exist and be equal to the function's value at that point.

One-sided Limits

One-sided limits analyze the behavior of a function as the input approaches a specific point from one direction only—either from the left or the right. They are especially important when a function might not have the same behavior on both sides of a point, which is key in identifying certain types of discontinuities.

Limits

Limits concern the behavior of a function as the input approaches a particular value. They help us understand how the function behaves near points of interest, regardless of whether the function is defined at that specific point.

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