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Answer Key and Solutions Part B

Answer Key and Solutions Part B - 6.AbsoluteValue y 1...

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y x 1 2 3 4 5 6 – 1 – 2 1 2 3 4 – 1 – 2 f(g(x)) x 1 2 3 4 5 6 – 1 2 4 – 2 f(x) x 1 2 3 4 5 1 2 6. Absolute Value 1. Local maximum of 2.25 at  x  = 3.5. Global maximum of  32 at  x  = - 2. Local and global minimum of 2 at  x  = 3 and  x  = 4. 2. x    - 0∙5. 7.  Limits 1. (a) 0.5   (b)   2.5   (c)   0 2. (a)   0   (b)    a 2 1 3. x lim   8 5 6 8 4 3 2 2 3 2 + - - + - x x x x x  =  x lim   2 2 8 5 6 8 4 3 2 x x x x x + - - + -    ü  = -    ü 8. Continuity and Differentiability 1. (a) x x g f - - = 3 3 )) ( ( (b) x  = 3. c (c) - < = 3 , 1 3 , 1 x x dx dy (d) Domain of  g  could be changed to  x    3. 2. x - - 5 2 1 3. (a) 3 10 (b) graph (c) The function is not differentiable at x = 2, x 3 10 =  and x = 4 as a corner occurs at each – there is no  unique tangent at each. 4. (a) < - - + + - - - + = 2 1 0 0 2 1 9 6 1 3 9 6 1 3 ) ( 2 2 x x x x x x x x x f     VET Calculus 141 21.Solutions
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(b) 1 ) ( 0 lim = x f x  and  1 ) 0 ( = f    so  ( x ) is continuous. (c) (i) < - - + - + - - - + - = 2 1 0 0 2 1 9 6 1 9 3 3 9 6 1 9 3 3 ) ( 2 2 x x x x x x x x x f (ii) ) 0 ( f is defined because  ) 0 ( ) 0 ( + - = f f   and  f  is continuous at  x  = 0. 5. (a) all reals  3 ± (b) < < - - - < = 3 2 3 3 2 3 2 ) ( x x x x x x x f 6. (a)   p=2   (b)   left hand derivative      right hand derivative 7. (a) 4.(a)   f (-1) = 2.
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