Question

1. Let $f$ be the function defined by $f(x) = ln|x|$ Which of the following statements is true? $circ$ $f$ is differentiable but not continuous at $x = 0$ $circ$ $f$ is not differentiable and not continuous at $x = 0$ $circ$ $f$ is differentiable and continuous at $x = 0$ $circ$ $f$ is differentiable but continuous at $x = 0$ 2. Which of the following statements must be true? (You may want to try and come up with some counter examples to figure it out.) $circ$ If a function is continuous, then it is differentiable $circ$ If a function is differentiable, then it is continuous $circ$ If the derivative of a function is not continuous, then the function is differentiable.

          1. Let $f$ be the function defined by
$f(x) = ln|x|$
Which of the following statements is true?
$circ$ $f$ is differentiable but not continuous at $x = 0$
$circ$ $f$ is not differentiable and not continuous at $x = 0$
$circ$ $f$ is differentiable and continuous at $x = 0$
$circ$ $f$ is differentiable but continuous at $x = 0$
2. Which of the following statements must be true? (You may want to try and come up with some counter examples to figure it out.)
$circ$ If a function is continuous, then it is differentiable
$circ$ If a function is differentiable, then it is continuous
$circ$ If the derivative of a function is not continuous, then the function is differentiable.

1. Let f be the function defined by
f(x) = ln|x|
Which of the following statements is true?
circ f is differentiable but not continuous at x = 0
circ f is not differentiable and not continuous at x = 0
circ f is differentiable and continuous at x = 0
circ f is differentiable but continuous at x = 0
2. Which of the following statements must be true? (You may want to try and come up with some counter examples to figure it out.)
circ If a function is continuous, then it is differentiable
circ If a function is differentiable, then it is continuous
circ If the derivative of a function is not continuous, then the function is differentiable.

Added by Nicholas S.

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