Given the following limit, select all statements that must be true. lim h→0 Select all that apply: f(x) is continuous at x = 1. ☐ f(x) is differentiable at x = 1. ☐ limf(x) exists. 0 lim f(x) = f(-1). f(−1 + h) − f(−1) h = 1
Given the following limit, select all statements that must be true. lim h→0 Select all that apply: f(x) is continuous at x = 1. ☐ f(x) is differentiable at x = 1. ☐ limf(x) exists. 0 lim f(x) = f(-1). f(−1 + h) − f(−1) h = 1
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Given the following limit, select all statements that must be true.**
\[
\lim_{{h \to 0}} \frac{{f(-1 + h) - f(-1)}}{h} = 1
\]
**Select all that apply:**
- [ ] \( f(x) \) is continuous at \( x = 1 \).
- [ ] \( f(x) \) is differentiable at \( x = 1 \).
- [ ] \( \lim_{{x \to 1}} f(x) \) exists.
- [ ] \( \lim_{{x \to 1}} f(x) = f(-1) \).
- [ ] None of the above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5ea397a-632d-4020-8701-e2de67ac8a17%2Fcaf5e4d1-0bd9-4848-b9cc-fd2868512bd1%2Fg85soep_processed.png&w=3840&q=75)
Transcribed Image Text:**Given the following limit, select all statements that must be true.**
\[
\lim_{{h \to 0}} \frac{{f(-1 + h) - f(-1)}}{h} = 1
\]
**Select all that apply:**
- [ ] \( f(x) \) is continuous at \( x = 1 \).
- [ ] \( f(x) \) is differentiable at \( x = 1 \).
- [ ] \( \lim_{{x \to 1}} f(x) \) exists.
- [ ] \( \lim_{{x \to 1}} f(x) = f(-1) \).
- [ ] None of the above.
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