Sample Calculus Quiz in LaTeX2HTML version

1. The following table gives the windchill W at various temperatures T, () and wind speeds v (mph).

   & & & & & & &
   

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   & T =15 & T =10 &T = 5 &T = 0
   

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   v= 15& -11 & -18 & -25 &-31
   

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   v= 20& -17 & -24 & -31 & -39
   

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   v= 25& -22 & -29 & -36 & -44
   

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   1. Use the table to find approximate values for , when T=0 and v=25.

   2. Using the table and your answers to a), give (an approximation of) the local linearization for W around T=0 and v=25.

   3. Use the local linearization to approximate W when T=-5 and v=25.

2. Suppose you are given two infinite wires which are parallel to the z-axis, passing through the points and in the xy plane which are homogeneously and oppositely charged. The potenial energy P of a unit charge in the xy plane is given by

   

   1. What is the gradient of the potential energy at ?

   2. What is the rate of change of P in the direction at ?

   3. An equipotential line is a curve along which the electrical potential is constant. What is the direction of the equipotential line passing through ?

   4. Another particle with a unit charge is moving up the y axis at a rate of . What is the rate of change of the potential energy of this particle?

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