Question Bank: Continuity and Differentiability

What is the definition of continuity at a point c for a function f?

Which of the following functions is continuous at x = 2?

At which point is the function f(x) = {2 if x < 1, 3 if x ≥ 1} discontinuous?

Which condition is necessary for differentiability at a point?

How do you identify a removable discontinuity in a function?

Which of the following functions is not continuous?

If f is continuous at c, which statement is always true?

Which of the following statements is false regarding continuity?

What does the Intermediate Value Theorem state?

A function can be differentiable at a point but not continuous at that point. True or False?

What is an example of a step function?

If a function f has a removable discontinuity at x = c, which of the following is true?

Which of the following characterizes a non-removable discontinuity?

Which theorem can help analyze the continuity of functions?

Which of the following is the domain of the exponential function f(x) = b^x, where b > 0?

What is the range of the exponential function f(x) = b^x, where b > 1?

Which of the following functions is continuous for all real numbers?

The value of b in the function f(x) = b^x must be:

To determine the continuity of f(x) = 3x - 4 at x = 2, what should you evaluate?

If f(x) = 2^x, what is the value of f(0)?

The function f(x) = x^2 - 3 is continuous because it is which type of function?

What can be inferred about the growth rate of f(x) = 10^x compared to polynomial functions?

At which point is the function f(x) = (x^2 - 1)/(x - 1) discontinuous?

What is the derivative of the function f(x) = e^x?

For f(x) = |x - 3|, what can be said about its continuity at x = 3?

Which of the following is the logarithmic form of the equation 2^3 = 8?

If f(x) = 2x + 5, what type of function is it regarding continuity?

If f(x) = x^2 and g(x) = 2^x, what is the growth comparison of f and g for large x?

Examine the function f(x) = 1/(x^2 - 4). Is it continuous?

What is the value of ln(e^5)?

For f(x) defined as f(x) = x + 1 if x ≤ 1 and f(x) = 3 if x > 1, is f continuous at x = 1?

What is the base of the natural logarithm?

Which statement correctly describes a continuous function?

Which function demonstrates logarithmic growth as opposed to exponential growth?

Which function is a classic example of a discontinuous function?

The inverse of the exponential function f(x) = b^x is:

The function f(x) = sqrt(x-1) is continuous at which of the following points?

What happens to f(x) = 1/b^x as x approaches infinity, where b > 1?

To prove that f(x) = x^3 - 2x^2 + x is continuous at x = 2, you must show what?

Which equation represents the relationship between exponential and logarithmic functions?

A function that is continuous everywhere is often termed what?

Consider the function f(x) = |x|. Is it continuous?