378 HW01_mathreview

378 HW01_mathreview - HW01 Math Review 1. Sketch the graphs...

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HW01 – Math Review 1. Sketch the graphs of the following functions (a) y=e x (b) y=e -x (c) y= ln x 2. Find the derivatives of the following functions (you do not need to simplify your answers to this section): (a) y= 1 2 x -5 (b) y= ( 1 2 x -3) 2 (c) y=5 (d) y= 2 2 4 x x (e) y= ln x (f) y = e ax (g) y = ln(x+3) 2 (h) y = x 2 e -2x (i) y = x 2 + 5x -8 3. List the first four terms of each of the following sequences (i=1,2,3…) (a) y i = i (b) x i = 2 i (c) z i = 3i 4. Evaluate the following summations using the definitions of sequences x i , y i , and z i given in (3): (a) = 3 1 i i y (b) 3 1 3 i i y = (c) 3 1 1 i i x = + (d) () = + 3 1 2 i i i z z (e) = + 3 1 2 5 2 1 i i x (f) 3 1 (2 ) ii i y z = + 5. Evaluate the following summations (a) 3 1 1 (1 ) n n p p = where p=0.25 (b) =
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378 HW01_mathreview - HW01 Math Review 1. Sketch the graphs...

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