Podcast
Questions and Answers
What can be done to remove a discontinuity of a function f at x = a?
What can be done to remove a discontinuity of a function f at x = a?
- Assign a suitable value to the function f at x = a (correct)
- Remove the function f from the domain
- Replace the function f with a different function
- Change the value of x to a different value
What can be said about the continuity of f + g and f - g if f is continuous at x = c and g is discontinuous at x = c?
What can be said about the continuity of f + g and f - g if f is continuous at x = c and g is discontinuous at x = c?
- f + g and f - g are discontinuous (correct)
- Both f + g and f - g are continuous
- Both f + g and f - g are discontinuous
- f + g is continuous, but f - g is discontinuous
What is the point of discontinuity of the function y = u + u - 2 where u = -1?
What is the point of discontinuity of the function y = u + u - 2 where u = -1?
- x = -2
- x = 2
- x = 1
- x = -1 (correct)
What is true about the function f(x) = 1/(x - 1)?
What is true about the function f(x) = 1/(x - 1)?
What is the domain of the function log(1 + ax) - log(1 - bx)?
What is the domain of the function log(1 + ax) - log(1 - bx)?
What is the meaning of the word 'Continuous' in mathematics?
What is the meaning of the word 'Continuous' in mathematics?
Which of the following functions is NOT continuous?
Which of the following functions is NOT continuous?
A function f(x) is said to be continuous at a point x=a if and only if:
A function f(x) is said to be continuous at a point x=a if and only if:
Which of the following functions is continuous on the entire real line?
Which of the following functions is continuous on the entire real line?
What is the condition for a function f(x) to be discontinuous at a point x=a?
What is the condition for a function f(x) to be discontinuous at a point x=a?
If a continuous function f(x) is defined on [a, b] and f(a) and f(b) are of opposite signs, then what can be concluded about the function?
If a continuous function f(x) is defined on [a, b] and f(a) and f(b) are of opposite signs, then what can be concluded about the function?
If a function f(x) is continuous on [a, b] and maps [a, b] into [a, b], what can be concluded about the function?
If a function f(x) is continuous on [a, b] and maps [a, b] into [a, b], what can be concluded about the function?
What is a necessary condition for the composite function y = (gof)(x) = g(f(x)) to be continuous at x = a?
What is a necessary condition for the composite function y = (gof)(x) = g(f(x)) to be continuous at x = a?
What type of discontinuity occurs when lim+ f(x) = lim- f(x) but their common value is not equal to f(a)?
What type of discontinuity occurs when lim+ f(x) = lim- f(x) but their common value is not equal to f(a)?
What is the condition for a function f to be discontinuous at x = a?
What is the condition for a function f to be discontinuous at x = a?
Which of the following functions is continuous on the entire real line?
Which of the following functions is continuous on the entire real line?
What can be said about the domain of the function f(x) = 1/(x^2 + 1)?
What can be said about the domain of the function f(x) = 1/(x^2 + 1)?
Let f(x) and g(x) be two continuous functions at x = a. Which of the following is continuous at x = a?
Let f(x) and g(x) be two continuous functions at x = a. Which of the following is continuous at x = a?
What can be said about the function f(x) = x^2 at x = 0?
What can be said about the function f(x) = x^2 at x = 0?
Let f(x) be a continuous function on [a, b]. What can be concluded about the function f(x)?
Let f(x) be a continuous function on [a, b]. What can be concluded about the function f(x)?
What can be said about the function f(x) = 2|x|, in terms of its continuity?
What can be said about the function f(x) = 2|x|, in terms of its continuity?
What is the domain of the function f(x) = 1/(sin(x) - 1), if it is continuous?
What is the domain of the function f(x) = 1/(sin(x) - 1), if it is continuous?
Which of the following functions has a discontinuity at x = 0?
Which of the following functions has a discontinuity at x = 0?
What can be said about the function f(x) = cos(x), in terms of its continuity?
What can be said about the function f(x) = cos(x), in terms of its continuity?
What is true about the function f(x) = |x|, in terms of its continuity?
What is true about the function f(x) = |x|, in terms of its continuity?
What is the domain of the function f(x) = |x - 2|?
What is the domain of the function f(x) = |x - 2|?
If f(x) = x^2 and g(x) = 1/x, then what is the domain of the composite function (fog)(x)?
If f(x) = x^2 and g(x) = 1/x, then what is the domain of the composite function (fog)(x)?
Which of the following functions is continuous on the entire real line?
Which of the following functions is continuous on the entire real line?
If f(x) = x^2 is continuous on [0, 1] and f(0) = 0 and f(1) = 1, then what can be concluded about the function?
If f(x) = x^2 is continuous on [0, 1] and f(0) = 0 and f(1) = 1, then what can be concluded about the function?
If f(x) is discontinuous at x = a, then what can be said about the limits of f(x) at x = a?
If f(x) is discontinuous at x = a, then what can be said about the limits of f(x) at x = a?
Flashcards are hidden until you start studying
