First exam practice sheet
Date of test Thursday, Oct. 16 in class
Material covered Chapter 6, sections 1, 2, 3, 4, 5
Ch 1 section 7
Ch 3 section 5
Allowable materials Calculator (no TI-89 or 92)
3”(5” index card of notes
Trigonometry formulas handout
Sample problems
1. Eliminate the parameter to express the equation in Cartesian form and sketch the curve. [pic] [pic]
2. Eliminate the parameter to express the equation in Cartesian form and state the domain and range of the Cartesian equation.
a. [pic] [pic]
b. [pic] [pic]
c. [pic] [pic]
3. For the parametric curve defined by the equation [pic]
a. For what values of t is the tangent line to the curve vertical?
b. What are the equations of the tangent lines from part (a)?
4. The parametric equation for a cycloid is [pic].
a. Find an equation of the tangent line to the cycloid at [pic]
b. Find the area under one period of the cycloid
5. Find the length of the parametric curve [pic] for [pic]
6. Set up an integral for the length of the curve [pic] for [pic]. Do not evaluate the integral.
7. Sketch the region enclose between the curves [pic] and [pic] and find its area.
8. Sketch the region in the first quadrant enclosed between the curves [pic], [pic], and the y-axis and find its area.
9. Find the area enclosed by one loop of the parametric curve [pic]
(hint: After setting up the integral, use the identity [pic])
[pic]
10. Use an integral to find the volume of the pyramid drawn:
[pic]
11. Sketch the region enclosed by the curves [pic] and [pic], and then find the volume of the solid generated by revolving this region about the y-axis.
12. Use an integral to find the volume of the frustrum of a cone drawn below.
[pic]
13. For the function [pic], whose graph is drawn below,
[pic]
a. Find the average value of the function over the interval [pic]
b. Estimate from the graph the value of x at which the function f takes on the average value.
14. A spring with natural length 5 cm is stretched to a length of 7 cm, requiring a force of 10 Newtons. How much work is done in this stretching?
15. A 1000 lb piano is raised up to the window of an apartment building in Chicago, a height of 120 ft. The cable that lifts it weighs 2 lb per foot. How much work is done?
16. Calculate the total hydrostatic force on the dam drawn below:
[pic]
17. Find the moments and center of mass of the lamina drawn below, bounded by the curves [pic], [pic], and the x-axis, with density [pic].
[pic]
1.
Answers:
2. [pic] [pic]
[pic]
3.
a. [pic] [pic]
b. [pic] [pic]
c. [pic] [pic]
4.
a. [pic] for any integer k
b. [pic]
5.
a. [pic]
b. [pic]
6. [pic]
7. [pic]
8.
[pic]
Area:[pic]
9.
[pic]
Area: [pic]
10. [pic]
11. 12
12.
[pic]
[pic]
13. Volume: [pic]
14.
a. [pic]
b. [pic]
15. 0.1 J
16. 134,400 ft. lb.
17. [pic]
18. [pic] [pic]
[pic]
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- nystce exam practice tests
- cosmetology license exam practice test
- git online exam practice paper
- git online exam practice 2019
- ftce professional exam practice test
- chemistry exam practice test
- nutrition final exam practice quiz
- clep exam practice test free
- practice sheet for writing numbers
- cfp exam practice test
- milady final exam practice test
- acs inorganic exam practice test