DIFFERENTIAL CALCULUS

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Last updated 5:41 AM on 6/11/26
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8 Terms

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Continuous Function

It is simply a smooth function that can be drawn in a graph continuously without lifting your pencil.

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  • limx→a f(x) exists

  • f(a) is defined

  • limx→a f(x) = f(a)

What are the requirements for a continuous function?

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Jump

What type of discontinuity is this?

<p>What type of discontinuity is this?</p>
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Point/Removable

What type of discontinuity is this?

<p>What type of discontinuity is this?</p>
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Infinite

What type of discontinuity is this?

<p>What type of discontinuity is this?</p>
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A

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Rolle’s Theorem

This theorem states that if a function f(x) is continuous and differentiable on a closed interval [a, b] and f(a) = f(b), then there exists a point c between point a and b where f’(c) = 0