ࡱ> EG DmE@ e bjbj "vg zzz$$$8 %&TTf& j/j/j//y9y9y9UTWTWTWTWTWTWT$URW{Tzy98y9y9y9{Tj// T1R1R1Ry9 Vj/^z/UT1Ry9UT1R 1RQRzQR/Z& 0$CQRqRT0TQRX=GXQRXzQR y9y91Ry9y9y9y9y9{T{TD!$L>$ (1) Find the domain and range of each of the following functions please. (a)  EMBED Equation.3  (b)  EMBED Equation.3  (2) Evaluate each of the following limits please. (a)  EMBED Equation.3  (g)  EMBED Equation.3  (b)  EMBED Equation.3  EMBED Equation.3  (h)  EMBED Equation.3  (c)  EMBED Equation.3  (i)  EMBED Equation.3  (d)  EMBED Equation.3  (j)  EMBED Equation.3  (e)  EMBED Equation.3  (k)  EMBED Equation.3  (f)  EMBED Equation.3  (l)  EMBED Equation.3  (3) Find  EMBED Equation.DSMT4  and simplify please. (a)  EMBED Equation.3  (i)  EMBED Equation.3  (b)  EMBED Equation.3  (j)  EMBED Equation.DSMT4  (c)  EMBED Equation.3  (k)  EMBED Equation.2  (d)  EMBED Equation.3  (l)  EMBED Equation.3  (e)  EMBED Equation.3  (m)  EMBED Equation.DSMT4  (f)  EMBED Equation.3  (n)  EMBED Equation.DSMT4  (g)  EMBED Equation.3  (o)  EMBED Equation.DSMT4   (h)  EMBED Equation.DSMT4  (p) (4) Find all relative max and min points if  EMBED Equation.DSMT4  (5) Find the volume of the largest right circular cylinder which may be inscribed in a sphere whose radius is 3 feet.  EMBED Equation.DSMT4   (6) (7) Find the value of  EMBED Equation.3  at x = 1 for the function  EMBED Equation.3  if  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  (8) Write an equation of the line tangent to each of the following at the indicated point. (a)  EMBED Equation.DSMT4  at x = 1. (b)  EMBED Equation.DSMT4  (c)  EMBED Equation.DSMT4  (9) Sketch a graph of  EMBED Equation.DSMT4  showing all max/min points and all inflection points. (10) Find all values of the constants a, b, and c if the graph of  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  are to be tangent to each other at the point (1 , 1). (11) Solve each of the following differential equations please. (a)  EMBED Equation.2  , the graph of y passes through (2 , 3) with slope 0. (b)  EMBED Equation.2  , y passes through (1 , 4). (12) Evaluate each of the following integrals please. (a)  EMBED Equation.2  (l)  EMBED Equation.2  (b)  EMBED Equation.2  (m)  EMBED Equation.2  (c)  EMBED Equation.2  (n)  EMBED Equation.2  (d)  EMBED Equation.2  (o)  EMBED Equation.2  (e)  EMBED Equation.2  (p)  EMBED Equation.DSMT4  (f)  EMBED Equation.2  (q)  EMBED Equation.DSMT4   EMBED Equation.2  (g)  EMBED Equation.2  (r)  EMBED Equation.DSMT4  (h)  EMBED Equation.2  (s)  EMBED Equation.DSMT4  (i)  EMBED Equation.2  (t)  EMBED Equation.DSMT4  (j)  EMBED Equation.2  (u)  EMBED Equation.DSMT4  (k)  EMBED Equation.2  (v)  EMBED Equation.DSMT4  Answers  (1) (a) (b) (2) (a)  EMBED Equation.DSMT4  (g)  EMBED Equation.DSMT4  (b) 32  EMBED Equation.3  (h)  EMBED Equation.DSMT4  (c)  EMBED Equation.DSMT4  (i)  EMBED Equation.DSMT4  (d)  EMBED Equation.DSMT4  (j)  EMBED Equation.DSMT4  (e)  EMBED Equation.DSMT4  (k)  EMBED Equation.DSMT4  (f)  EMBED Equation.DSMT4  (l) 2 Answers (3) (a)  EMBED Equation.DSMT4  (i)  EMBED Equation.DSMT4  (b)  EMBED Equation.DSMT4  (j)  EMBED Equation.DSMT4  (c)  EMBED Equation.DSMT4  (k)  EMBED Equation.DSMT4  (d)  EMBED Equation.DSMT4  (l)  EMBED Equation.DSMT4  (e)  EMBED Equation.DSMT4  (m)  EMBED Equation.DSMT4  (f)  EMBED Equation.DSMT4  (n)  EMBED Equation.DSMT4  (g)  EMBED Equation.DSMT4  (o)  EMBED Equation.DSMT4  (h)  EMBED Equation.DSMT4  (p)  EMBED Equation.DSMT4  (4) max. at  EMBED Equation.DSMT4  , min. at (0 , 0) (5)  EMBED Equation.DSMT4  Answers (6)  EMBED Equation.DSMT4  (7) 180 (8) (a)  EMBED Equation.DSMT4  (b) y = 2 (c)  EMBED Equation.DSMT4  (9) Graph (10) a = 2 , b = 2 , c = 2 (11) (a)  EMBED Equation.DSMT4  (b)  EMBED Equation.DSMT4  Answers (12) (a)  EMBED Equation.DSMT4  + C (l)  EMBED Equation.DSMT4  + C (b)  EMBED Equation.DSMT4  + C (m)  EMBED Equation.DSMT4  + C (c)  EMBED Equation.DSMT4  + C (n)  EMBED Equation.DSMT4  + C (d)  EMBED Equation.DSMT4  + C (o)  EMBED Equation.DSMT4  + C (e)  EMBED Equation.DSMT4  + C (p)  EMBED Equation.DSMT4  + C (f)  EMBED Equation.DSMT4  + C (q)  EMBED Equation.DSMT4  + C (g)  EMBED Equation.DSMT4  + C (r)  EMBED Equation.DSMT4  + C (h)  EMBED Equation.DSMT4  + C (s)  EMBED Equation.DSMT4  + C (i)  EMBED Equation.DSMT4  + C (t)  EMBED Equation.DSMT4  + C (j)  EMBED Equation.DSMT4  + C (u)  EMBED Equation.DSMT4  + C (k)  EMBED Equation.DSMT4  + C (v)  EMBED Equation.DSMT4  + C Calculus Midterm Review Sheet  EMBED Equation.DSMT4  5 2 2 3 Water is pouring into the trough to the right at a constant rate of 2 cubic feet per minute. Each base is an inverted isosceles triangle with base 2 feet and height 3 feet as shown. How fast is the depth of the water changing at the instant when the trough is  EMBED Equation.DSMT4  full by volume? 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