Continuity and Differentiability Quiz
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Preview questions
1. Which of the following functions is continuous at x = 1?
f(x) = 1/x · f(x) = x^2 · f(x) = sin(x) · f(x) = ln(x)
2. If f(x) is continuous at x = a, which of the following must be true?
f(a) exists · f(a) = f(a+) · f(a) = f(a-) · All of the above
3. A function is differentiable at a point if it is:
Continuous at that point · Not continuous at that point · Piecewise defined · None of the above
4. The derivative of a function at a point gives the:
Slope of the tangent · Value of the function · Area under the curve · Rate of change of area
5. Which of the following is a necessary condition for differentiability?
Continuity · Existence of limits · Existence of derivatives · All of the above
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