Maple 19 SVDiff Calc Workbook Solutions.mw

• Chapter 1: Where to Start?
• Chapter 2: Canny and Calculating
  • NULL
  • #2 Given a = 3, b = -1 and c = -2,  find the value of:
  • #3.    Given a = -x^2 + 3, b = -1/xand c=-2+x, find the value of:
  • #4.    Factor:
  • #5.    Expand:
  • #6.    Condense:
  • #7.    Prove the trigonometric identities:
  • [Untitled Section]
• Chapter 3: Plotting and Solving
  • 1. Solve for x. Verify the solution with a graph.
  • 2. Solve using the Equation Manipulator and Drag to Solve.
  • 3. Solve the inequality
  • 4. Determine x + y  for eachx, y in a solution to:
  • 5. Find all solutions to x^sin(x) - 1 = 0  on [0, 10] .
  • Maple Problem Set
• Chapter 4: Define and Describe
  • 1.         Given  f(x)=(4 x-1)/(2 x+3),determine f^(-1)(-5).
  • 2.          Assume 0 <= theta and theta <= Pi/2.  Given theta = arctan(5/12), determine sin(theta).
  • 3.          Assume 0 <= theta and theta <= Pi/2.  Given theta = arccos(sqrt(x)/(x + 1)), determine tan(theta)and tan(2 theta).
  • 4.          Given Bob(x) = 2^x  and Milly(x) = x^2 + 1   , determine:
  • 5. Define a piecewise function for the following image:
  • 6. Recreate the image, with the points, in Maple.
  • 7. Determine the inverse of the function. Do you notice anything interesting about the slope values?
  • 8. Plot the function and its inverse, andy=x  on the same image.
  • 9. Use symmetry to plot the function and its inverse to create the following image:
• Chapter 5: Getting Closer and Closer
  • 1. Numerically determine(lim)((sin(x))/(x)).
  • 2. Consider f(x) = sin(x)/x .  Does it have a discontinuity? Create a plot. If a discontinuity exists, highlight it on the image.
  • 3. Determinelimit(sin(x)/x, x = 0) using the limit() command.
  • 4.        Given that cos(x) <= sin(x)/x and sin(x)/x <= 1
  • 5. Evaluate the limit or determine that it does not exist. State a reason why. Use a graph to back up all conclusions.
  • 6. Determine what value of the constant ‘ a ‘ makes the function f(x) = piecewise(1 <= x, 3*x^2, x < 1, a*x - 4)   continuous everywhere.
  • 7. Determine the equation of a function where the following conditions are met:
  • 8. Using the Limit Tutor determine: (lim)sqrt(a*x + x^2) - sqrt(b*x + x^2)
  • Maple Problem Set
• Chapter 6: The Instantaneous Rate of Change
  • 1.          Given f(x) = x^x
  • 2. Use the diff() and D() commands to determine the first and second derivatives of the following:
  • 3. Use the Calculus Palette to determine the first and second derivatives of the following:
  • 4. Determine the nth derivative:
  • 5. There are two tangent lines to f(x) = 3*x^2 - 13*x - 10   that passes through the point P(-1,-6).
  • 6.           Use the DerivativeTutor() to create a plot of f(x) = 3*x^2 - 13*x - 10 and the first derivative.
  • 7. Use the DiffTutor() to determine the first derivative of f(x)=((3 x+5)^(2))/((e)^(x)).
  • 8.         Given -x*y^3 + 2*x^3 + x^2*y = 2 and y = ln(2*x + 2*y):
  • 9.   Use the Tangent() function to determine the equation of a tangent line tof(x) = (3*x + 5)^2/exp(x)at x = -2.Verify the solution with a plot.
  • 10.        Find the cubic equation f(x) = ax^3 + bx^2 + cx + d given there is a maximim at 3, 8  and a min at -5, -2.
• Chapter 7: Curve Sketching
  • 1. Perform a full curve sketching analysis on f(x) = (x^2)^(1/3) + sin(x)limited to the interval  [-2,8].
  • 2. Given f(x) = exp(sin(x)) + x/2limited to the interval  [-10,10].
  • 3.           Given f(x) = x^sin(x)
• Chapter 8: Derivative Applications
  • 1.        Given the point 4, 1, which point on f(x) = sqrt(x) is the closest to it?
  • 2.       Given f(x) = sqrt(-x^2 + 36)determine all values that satisfy the MVT on the interval  [-3, 5] .
  • 3.       Given f(x, y) = ln(2*x + 2*y) determine all values that satisfy the MVT on the interval from point  P((exp(1/2) - 1)/2, 1/2)  to point  Q(((e)^(3))/(2)-3, 3).  
  • 4.       A conveyor belt is dumping corn into a large empty silo, forming a circular based cone shaped - heap on the floor. The base radius is twice the size of the height of the pile. If the corn is filling in the space at a rate of 2 m^3/ minute, find the rate at which the height is changing when the height is 3 m deep.
  • 5.      Housing developers hoping to attract buyers will often build in amenities for community members to enjoy. In a particular community, fishing is a key attraction, so the housing developers agree to build a small lake and stock it with trout. The population of trout over time can be modeled by p(t) = 1200/(1 + 29*exp(-0.36*t)),   where time is measured in months.
  • 6.       Solve exp(0.5*x) = x + 3 using Newton's Method.
  • [Untitled Section]
• Chapter 9: Explore
  • 1. Determine limit(sqrt(x^2 + ax) - sqrt(b*x + x^2), x = infinity)  using the Explore Command
  • 2. Given the Cartesian Equation for the Pearls of Sluze  y^n = k*(a - x)^p*x^m
  • 3. Givenf(x)=A*x^(2)+B*x+C.  Use Explore to create a graph of the function and the corresponding tangent line at x = a .
  • 4. Given f(x)=A*x^(3)+B*x^(2)+C*x.  Use Explore with the ExtremePoints() command  where x = -10 .. 10.
  • 5.           Given      f(x)=A*x^(3)+B*x^(2)+C*x.   Use Explore with the MeanValueTheorem() command where x = -10 .. 10.