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MC 2025 In-course Diagnostics for Undergraduate Mathematics MATH140 WP

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The function given by is differentiable at   What is the value of

Hint: Differentiability implies continuity.  Use the conditions for differentiability and continuity (i.e. limits from the left and right of x=0 must be equal) to find the values of m and n.

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If is a known positive integer, for what value of is ?
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If is a non-negative integer, then for:

(Hint: Let )

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What is the value of (Hint: Let ).

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The graph of the function pictured below consists of four semicircles.  If where is non-negative?

Quiz13Q7graph

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What is the value of

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True of False ?

If is continuous on , then the value of the Riemann Sum does not depend on the choice of , where

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For what does represent?

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If is differentiable at , which of the following could be false?
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If is a continuous function for all real , then is:
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