MATHS2001 Modelling and Change

MATHS2040 Engineering Mathematics Semester 1, 2017

Assignment

Due date: Wed, May 3, 2017 - 16:00

Worth: 15% of the final assessment

Note: Show the working in your answers.

1. (2 marks) Use Maclaurin series to evaluate the following limit

2. (3 marks) A panda population growth in a small reserve is given by the logistic equation

where t is in months. Here P(t) is the population of pandas at time t. The carrying capacity of the reserve is 75 pandas. Determine the amount of time for the number of pandas to reach 99% of the carrying capacity. Use Euler’s method with step size h = 1. Include the printout of the first page of Excel calculations and the graph of the obtained numerical solution.

3. (4 marks) A solid is obtained by cutting the top of the cone by a plane parallel to its base. Suppose it has a base with radius R, a top with radius r and a height h (see the figure below). Find the volume of this solid by rotating about the x-axis the region below the line segment from (0,R) to (h,r).

4. (4 marks) Solve the boundary-value problem, if possible

y00 + 4y0 + 29y = 0, y(0) = 1, y(p/2) = -e-p

5. (2 marks) Find the radius of convergence of the following series:

Federation University Australia

MATHS2040 Engineering Mathematics Semester 1, 2017

Assignment

Due date: Wed, May 3, 2017 - 16:00

Worth: 15% of the final assessment

Note: Show the working in your answers.

1. (2 marks) Use Maclaurin series to evaluate the following limit

2. (3 marks) A panda population growth in a small reserve is given by the logistic equation

where t is in months. Here P(t) is the population of pandas at time t. The carrying capacity of the reserve is 75 pandas. Determine the amount of time for the number of pandas to reach 99% of the carrying capacity. Use Euler’s method with step size h = 1. Include the printout of the first page of Excel calculations and the graph of the obtained numerical solution.

3. (4 marks) A solid is obtained by cutting the top of the cone by a plane parallel to its base. Suppose it has a base with radius R, a top with radius r and a height h (see the figure below). Find the volume of this solid by rotating about the x-axis the region below the line segment from (0,R) to (h,r).

4. (4 marks) Solve the boundary-value problem, if possible

y00 + 4y0 + 29y = 0, y(0) = 1, y(p/2) = -e-p

5. (2 marks) Find the radius of convergence of the following series:

Federation University Australia

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