Podcast
Questions and Answers
Which of the following functions is continuous at x=0?
Which of the following functions is continuous at x=0?
- f(x) = -x for x < 0 and f(x) = -x for x ≥ 0
- f(x) = e for x < 0 and f(x) = e for x ≥ 0
- f(x) = e^(-x) for x < 0 and f(x) = -x for x ≥ 0 (correct)
- f(x) = e for x < 0 and f(x) = -x for x ≥ 0
At which point is the function g(x) not continuous?
At which point is the function g(x) not continuous?
- g(-1)
- g(1)
- g(2)
- g(0) (correct)
What is the value of f(0) if f(x) = e for x < 0 and f(x) = -x for x ≥ 0?
What is the value of f(0) if f(x) = e for x < 0 and f(x) = -x for x ≥ 0?
- Undefined
- 0
- 1 (correct)
- e
Which statement regarding continuity at x=-3 for the function f(x) is true?
Which statement regarding continuity at x=-3 for the function f(x) is true?
Which of the following functions is defined but not continuous at its specified point?
Which of the following functions is defined but not continuous at its specified point?
For the function k(x) described, where is the function continuous?
For the function k(x) described, where is the function continuous?
Which of the following is a requirement for continuity at a point?
Which of the following is a requirement for continuity at a point?
Which function is continuous everywhere except at x=-3?
Which function is continuous everywhere except at x=-3?
Flashcards
Continuity at a point
Continuity at a point
A function is continuous at a point if the limit of the function as x approaches that point exists and equals the function's value at that point.
Function continuous on domain
Function continuous on domain
A function is continuous on its domain if it is continuous at every point within its domain.
Continuity Characteristics
Continuity Characteristics
A function is continuous at a point only if: 1) the function is defined at that point; 2) the limit of the function as x approaches that point exists; and 3) the limit equals the function's value at that point.
Continuity on an interval
Continuity on an interval
Signup and view all the flashcards
Function continuous at x=a
Function continuous at x=a
Signup and view all the flashcards
Function discontinuous at x=a
Function discontinuous at x=a
Signup and view all the flashcards
Limit of a function
Limit of a function
Signup and view all the flashcards
Piecewise Function
Piecewise Function
Signup and view all the flashcards
Study Notes
General Math (I) - Lecture 7
- Topic: Continuity of Functions
- Chapter: 2 - Functions & Limits
- Key Concepts: Continuity, Limits, Functions
- Study points
- Continuity at a point
- A function f is continuous at x = a when:
- f(a) is defined
- lim (x→a) f(x) exists
- lim (x→a) f(x) = f(a)
- If any condition is not met, the function is not continuous at x = a.
- Continuity on domains
- Constant functions
- Polynomial functions
- Exponential functions
- Absolute value functions
- Odd root functions (e.g., cube root)
- Sine and cosine functions
- Continuity characteristics
- Sums (f + g)
- Differences (f - g)
- Products (f â‹… g)
- Constant multiples (k â‹… f, where k is any number)
- Quotients (f/g, provided g(c) ≠0)
- Powers (fr/s, provided it is defined on an open interval containing c, where r and s are integers)
- Continuity on an interval
- A function is continuous on a closed interval if it is continuous at all interior points and the endpoints.
- A function f is continuous on the closed interval [a, b] if:
- f is defined on [a, b]
- f is continuous on (a, b)
- lim (x→a+) f(x) = f(a)
- lim (x→b-) f(x) = f(b)
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Explore the concept of continuity in functions in this lecture quiz. Delve into the conditions that define continuity at a point and learn about various types of functions, including polynomial and exponential. This quiz will test your understanding of limits and characteristics of continuous functions.
