# Sketch the following functions; be sure to label the axes...

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CBE 320 September 7, 2016 Introductory Transport Phenomena Problem Session I Part B: Review of Mathematical Topics Review Appendices A and C in Introductory Transport Phenomena before doing this assignment. 1. Sketch the following functions; be sure to label the axes carefully. a. y ( x )= cosh bx cosh b , −∞ <x< , b = constant b. y ( x )= e bx , −∞ <x< , b = constant c. y ( x )= tanh x x , −∞ <x< d. v z ( r ) = v 0 bracketleftbigg 1 parenleftBig r R parenrightBig 2 bracketrightbigg , 0 r R, v 0 ,R = constant e. v z ( r ) = v 0 ln( r/R ) ln κ , κR r R, v 0 ,R,κ = constant , 0 <κ< 1 2. A particle is located at x =2 , y =2 , z =1 in Cartesian (rectangular) coordinates. a. What are the cylindrical coordinates of the particle ( r,θ,z ) ? b. What are the spherical coordinates of the particle ( r,θ,φ ) ? 3. A particle, located at x =2 , y =4 , z =0 , is moving with velocity v =2 δ x +2 δ y . a. What is | v | ? b. Carefully sketch the vector v , using one unit of each distance and velocity equal to 1 (see Fig. A.6-2). Indicate the cartesian components (
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