Calculus
1 Final Exam
- Math 220 Fall,
2006
1. |
Sketch the parabola given by y = x2 + 6x 1. Find its vertex and x and y intercepts. Answers: y-intercept = -1 x-intercepts at -3 ± √10 |
2. |
Use the definition of the derivative to find df/dx for each x for the function, f(x) = 2x 3. |
3. |
Write the equation of the line tangent to the curve y = 4 x 2/3 at (1,4). Answer: y = (8/3) x + 4/3 |
4. |
Starting from xo = 1, find x1 and x2 using Newtons method to approximate solution of the equation f(x) = 2 ln x - 2 + x. Answers: x1 = 4/3 x2 = 4/3 (2/5) [ 2 ln(4/3) 2/3 ] |
5. |
Find the intervals of convexity (up, down) of the function f(x) = 2x3 9x2 102 x + 5. Answers: Concave up for x > 3/2 Concave down for x < 3/2 |
6. |
Find the derivative of y = arcos x. Answer: dy/dx = -1 / √ (1 x2 ) |
7. |
Use the method of cross-sections (disks) to find the volume of the solid generated by rotating around the y-axis the region bounded by the curves x= 0, y = x, and y = 3 2x. Answer: V = π. Click here to continue with this exam. |