## Math 122 - Exam 7 Study Guide (11.8 - 12.5)

1. Find the radius of convergence and the interval of convergence for the given series.
2. Find the third Taylor polynomial for the given function about the given point.
3. Find Lagrange's form of the remainder.
4. Use the Maclaurian series table to obtain the Maclaurian series for the given function. Two parts.
5. Use an appropriate Taylor series to approximate a function.
6. Rotate the axes to eliminate the xy-term. Sketch the graph of the resulting equation, showing both sets of axes.
7. Application problem involving a parabola.
1. Find the equation of the parabola given the focal length.
2. Find the ordinates of a point on the parabola given an abscissa.
3. Find the angle of rotation to point the axis of symmetry at another object.
4. Sketch the rotated parabola. Note - you do not need to find the equation of the rotated parabola, just take the one in standard position and rotate it through the angle found in part 3.
8. Given the equation of an ellipse ...
1. Find the area
2. Find the volume of the prolate spheroid
3. Find the volume of the oblate spheroid
9. Application problem involving a hyperbola. The problem is similar to 12.4.49 and involves finding the equation of the hyperbola, given the difference in times something is heard between two points. After finding the equation of the hyperbola, sketch its graph.

### Notes:

• Problems 1 - 5 are directly from the text.
• Problems 6, 8, and 9 are from the Larson text.
• Problem 7 is a satellite dish problem using data from the Internet.