Relationship between differentiability and continuity

Practice Questions

AP Calculus AB › Relationship between differentiability and continuity

Questions

4

1

For which of the following functions does a limit exist at , but not a y-value?

2

Which of the following functions is differentiable at , but not continuous there?

3

The function is differentiable at the point . List which of the following statements must be true about :

1) The limit $\lim_{x->a}\frac{f(x)-f(a)}{x-a}$ exists.

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2) $\lim_{x->a^{-}}f(x)=\lim_{x->a^{+}}f(x)$

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3) $\lim_{x->a}\frac{f(x)-f(a)}{x-a}=f(a)$

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4) $\lim_{x->a}f(x)=f(a)$

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5) $\lim_{x->a}f(x)=\lim_{x->a}\frac{f(x)-f(a)}{x-a}$

4

When the limit $\lim_{h \to 0} \frac{f(2+h)-f(2)}{h}$ fails to exist,

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