Calculus homework help

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Math 1325 final exam due today
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    Math 1325 – Final Exam
    Chapters 11, 12, 13, 14
     
     
     
    Name                                  
    NO CELL PHONES
    NO GRAPHING CALCULATORS PLEASE
     
     
     
    MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.
     
    Find the partial derivative as requested.
    1) fy(5, -6)  if f(x,y) = 7×2 – 9xy                                                                                                                                1)                                                                                                                                                                                                                    A) 129                                  B) -54                                  C) -45                                 D) 39
     
     
    Find the second–order partial derivative.
    2) Find fyx when f(x,y) = 8x3y – 7y2 + 2x.                                                                                                              2)                                                                                                                                                                                                                             

    1. A) 48xy B) -14                                  C) -28                                 D) 24×2

    Solve the problem.
    3) The profit from the expenditure of x thousand dollars on advertising is given by                                       3)
    P(x) = 930 + 25x – 4×2. Find the marginal profit when the expenditure is x = 9.

    1. A) 225 thousand dollars/unit B) 153 thousand dollars/unit
    2. C) 930 thousand dollars/unit D) -47 thousand dollars /unit

    4) Find C(x) if C'(x) = 5×2 –  7x + 4 and C(6) = 260.                                                                                                4)                                                                                                                                                                                                                             

    1. A) C(x) = 5x3 –  7 x2 + 4x + 2                                        B) C(x) =  5 x3 –  7 x2 + 4x – 2

    3         2                                                                            3         2

    1. C) C(x) = 5x3 –  7 x2 + 4x – 260                                   D) C(x) =  5 x3 –  7 x2 + 4x + 260

    3         2                                                                            3         2
     
    5) The revenue generated by the sale of x bicycles is given by R(x) = 50.00x –  x2 . Find the marginal
    200
    5)                   
    revenue when x = 600 units.

    1. A) $100/unit B) $50.00/unit                    C) $56.00/unit                    D) $44.00/unit

    6) The rate at which an assembly line worker’s efficiency E (expressed as a percent) changes with              6)
    respect to time t is given by E'(t) = 70 – 6t, where t is the number of hours since the worker’s shift
    began.  Assuming that E(1) = 92, find E(t).

    1. A) E(t) = 70t – 3t2 + 25 B) E(t) = 70t – 3t2 + 92
    2. C) E(t) = 70t – 6t2 + 25 D) E(t) = 70t – 3t2 + 159

    Identify the intervals where the function is changing as requested.
    7) Increasing                                                                                                                                                               7)

    1. A) (-2, -1) 1 (2, Q) B) (-1, Q)                            C) (-2, -1)                           D) (-1, 2)

     
     
    Determine the location of each local extremum of the function.
    8) f(
     
     
     
     
     
     

    x) = -x3- 4.5×2 + 12x + 4 8)                   
    A) Local maximum at 1; local minimum at -4  
    B) Local maximum at -4; local minimum at 1  
    C) Local maximum at -1; local minimum at 4  
    D) Local maximum at 4; local minimum at -1  

     

    Find the equation of the tangent line to the curve when x has the given value.
    9) f(x) = 5×2 + x ; x = -4                                                                                                                                              9)                                                                                                                                                                                                                             

    1. A) y = x +  1
    1. B) y = 13x – 16 C) y = -39x – 80                 D) y = –  4x +  8

    20     5
    25     5
     
    Find the largest open interval where the function is changing as requested.
    10) Increasing    f(x) = x2 – 2x + 1                                                                                                                              10)                                                                                                                                                                                                                   A) (-Q, 0)                             B) (0, Q)                              C) (-Q, 1)                            D) (1, Q)
     
     
    Find dy/dx by implicit differentiation.
    11) 2xy – y2 = 1                                                                                                                                                            11)                                                                                                                                                                                                                               

    1. A)   x   

    y – x

    1. B)   x   

    x – y

    1. C)   y   

    x – y

    1. D)   y   

    y – x
     
    Find the area of the shaded region.
    12)                                                                                                                                                                                  12)

    1. A) 5

    3

    1. B) 3 C) 5                                     D)  23

    3
     
    Use the properties of limits to evaluate the limit if it exists.
    13)   lim x    6
       x + 6    (x – 6)2
    13)                 

    1. A) 0 B) 6                                     C) -6                                   D) Does not exist

    14)  lim   x3 + 12x2 – 5x
    x  0
    14)
    5x

    1. A) 0 B) Does not exist               C) -1                                   D) 5

     
     
    Evaluate.

    a

    15)          34  dx                                                                                                                                                              15)                                                                                                                                                                                                                               
    x2

    1. A) 34x + C B)  34 + C                            C) -34x + C                        D) –  34 + C

    x                                                                                          x
     
    Find the integral.

    a

    16)            19     dy                                                                                                                                                         16)                                                                                                                                                                                                                               
    2 + 5y

    1. A) 18ln  2 + 5y  + C                                                       B)  19 ln  2 + 5y  + C

    5                                                                                       5
     

    1. C) 19 ln 2 + 5y + C                                                       D) 18 ln  2 + 5y  + C

     
    17)  a   8x – 9x-1  dx                                                                                                                                                  17)                                                                                                                                                                                                                    A) 4×2 – 9 ln  x  + C                                                        B) 4×2 +  9 x-2 + C
    2

    1. C) 16×2 – 9 ln x + C                                                     D) 16×2 +  9 x-2 + C

    2
     

    a

    18)              x dx       (7×2 + 3)5

    1. A) – 1 (7×2 + 3)-4 + C                                                   B) –  1  (7×2 + 3)-6 + C

    18)                 
    56
                     -4
    14
     7               -6

    1. C) – 7 (7×2 + 3)

    3
    + C                                                    D) –
    (7×2 + 3)     + C
    3
     
    19)  a 9z    3z2 – 7 dz                                                                                                                                                  19)                                                                                                                                                                                                                    A) z(3z2 – 7)3/2 + C                                                           B) (3z2 – 7)3/2 + C
                        3/2
     1               3/2

    1. C) 1 z(3z2 – 7)

    2
    + C                                                    D)
    (3z2 – 7)      + C
    2
     
    Find the absolute extremum within the specified domain.
    20) Maximum of f(x) = x2 – 4; [-1, 2]                                                                                                                        20)                                                                                                                                                                                                                    A) (-1, 3)                             B) (-2, 0)                             C) (1, -3)                             D) (2, 0)
    Assume x and y are functions of t. Evaluate dy/dt.
    21) x3 + y3 = 9;  dx = -5, x = 2                                                                                                                                    21)                                                                                                                                                                                                                               
    dt

    1. A) 20 B)  5

    4

    1. C) 4

    5

    1. D) – 20

     
    Use the given graph to determine the limit, if it exists.
    22)
    22)
    lim
    x  0-
    f(x) and  lim
    x  0+
    f(x).

    1. A) -1; 1 B) 1; -1                                C) 1; 1                                 D) -1; -1

     
     
    Find the derivative of the function.
    23) y = (3×2 + 5x + 1)3/2                                                                                                                                               23)                                                                                                                                                                                                                               

    1. A) y’ = (6x + 5)(3×2 + 5x + 1)1/2 B) y’ = (3×2 + 5x + 1)1/2

     

    1. C) y’ = 3(3×2 + 5x + 1)1/2                                              D) y’ =  3 (6x + 5)(3×2 + 5x + 1)1/2

    2                                                                                       2
     
    24) y = ln (3×3 – x2)                                                                                                                                                     24)                                                                                                                                                                                                                               

    1. A) 3x – 2  

    3×2 – x

    1. B) 9x – 2  

    3×3 – x

    1. C) 9x – 2  

    3×2 – x

    1. D) 9x – 2

    3×2
     
    Find the derivative.
    25) y = e5x2 + x                                                                                                                                                            25)                                                                                                                                                                                                                    A) 10xe + 1                          B) 10xe2x + 1                      C) 10xex2 + 1                     D) 10xe5x2 + 1
     
     
    26) f(x) = 20×1/2 –  1 x20                                                                                                                                               26)                                                                                                                                                                                                                               
    2

    1. A) 10×1/2 – 10×19 B) 10×1/2 – 10×10              C) 10x-1/2 – 10×19            D) 10x-1/2 – 10×10

    Find the general solution of the differential equation.
    27)  dy  = x – 2                                                                                                                                                               27)                                                                                                                                                                                                                               
    dx

    1. A) x2– x + C                      B) x3 – 2x + C                    C) 2×2 – 2 + C                    D)  x2 – 2x + C

    2                                                                                                                                    2
     
    Evaluate f”(c) at the point.
    28) f(x) =  3x – 4 ,  c = 1                                                                                                                                                 28)                                                                                                                                                                                                                               
    4x – 3

    A) f”(1) = -56 B) f”1) = 7 C) f”(1) = 44 D) f”(1) = 32  
     
     
    29) f(x) = ln (4x – 3),  c = 1
    A) f”(1) = 1    		  
     
    B) f”(1) = 0    		  
     
    C) f”(1) = 4    		  
     
    D) f”(1) = -16    		  
    29)

     
    Find the largest open intervals where the function is concave upward.
    30) f(x) = x3 – 3×2 – 4x + 5                                                                                                                                          30)                                                                                                                                                                                                                    A) (-Q, 1)                             B) None                              C) (1, Q)                              D) (-Q, 1), (1, Q)