Test 1 - 31L Test #" (Tomberg, spring 09) Name:_ I...

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31L Test # " (Tomberg, spring 09) Name:_______________________________ I reaffirm the Duke Community Standard. You must clearly show all your work on each problem to receive full credit. Unsupported work may receive no credit . 1. (a) State the definition of the derivative of the function at the point C& 5—B ± B& -² (b) , find the derivative of the function at the point 3. Using the definition C & B& 4 B # 2. (a) Let . Find and . 4 2, 3 8, 3 1 ,3 0—B± & ³ 0—B ± 0—B± B ´ B & ± ² 2 33 3 li m m lim B ˜ ´ (b) For what value(s) of will the following limit exist? 21 3 : B ¶:B´ 3 2 3. The temperature (C ) of a chemical reaction at time (sec.) can be modeled by the function ° >
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12log ( 6). (Note: This is NOT .) at 1 second. X & > ± 69 1 6 8 >& Estimate .X .> 4. In this problem you are to construct a mathematical model from a table of data. The table is shown below, but only two data points are filled in. > C 2 ?? 1 5 ???? 5. 5?? 464. 1???? The following are descriptions of some plots made from the complete table of data: If we plot the points (, ), we see a rising curve, which is concave up. >C If we plot the points ( , ), we see a rising curve, which is concave down. ln If we plot the points (ln , ), we see a line with positive slope. ln State what type of function would best model the relationship between and .
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Test 1 - 31L Test #" (Tomberg, spring 09) Name:_ I...

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