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Unformatted text preview: Math 1550 Test Four Review (Sections 4.6, 4.7, 4.8, 4.9, 5.1, and 5.2) F ind each limit. Use L Hospital ’3 Rule where appropriate. 5.1:
1. lim ﬂu;— 2. Iim x tan 3. lim (cos x)%‘ x—>O x2 xaw x xao Draw a diagram and label. Use calculus to solve. 7. A fence 8 ft tall runs parallel to a tall building at a distance of 5 feet from the building. What is the
length of the shortest ladder that will reach ﬁom the ground over the fence to the wall of the building? 8. A piece of wire 50 it long is cut into, at most, 2 pieces. If one piece is bent to from a circle and the
other is bent to form a square, determine how the wire should be cut in order that the total enclosed area is a
maximum or a minimum? 9. A rancher has 500 yd of fence with which to build a rectangular corral. Some of the fencing will be
used to construct two internal divider fences, both parallel to the same two sides of the corral. What is the
maximum possible total area of such a corral? 10. A square piece of sheet metal is 42 cm on a side. Equal squares are cut from its four corners. The resulting piece of metal is to be folded and welded to form an open—topped box. What size square should be
cut from each corner to have a box of largest possible volume? 11. A cardboard box of 108 in3 volume with a square base and open top is to be constructed. Find the
minimum area of cardboard needed. 12. Use Newton’s Method to approximate the root of COS x = 2x — 1 correct to eight decimal places.
Write the formula for x11“. F ind the antidertvattve of each. 13. f(x)=x3—Seczx—2 14. f(x)=3sinx—4x/——2
x Evaluate the indeﬁnite integrals. 15. j(3ex—cosx+x}1x 16. {$de 17. [x2(1—x+4x3)ax 18 Given f”(x) = sex — 23in x, f(0) = 5, f’(0) = —1, ﬁnd f(x). 19. Estimate the area under the graph of f (x) = 2 + x2 on the interval [1, 3] using 4 rectangles and the right endpoints of each subinterval. Sketch the graph of f and draw the rectangles on the graph.
Write the answer as a fraction. IS this an overestimate or an underestimate of the area? 20. Estimate the area under the graph of f (x) m 5 — x2 on the interval [0, 2] using 4 rectangles and the left endpoints of each subinterval. Sketch the graph of f and draw the rectangles on the graph.
Write the answer as a fraction. Is this an overestimate or an underestimate of the area? 3 21. Use the limit deﬁnition of the deﬁnite integral to evaluate K2 ~3x2 Show all steps.
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4 22. Evaluate J[1+ V16 — x2 )dx in terms of areas. Sketch the graph. Write answer in exact form.
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This note was uploaded on 07/21/2008 for the course MATH 1550 taught by Professor Wei during the Spring '08 term at LSU.
 Spring '08
 Wei
 Calculus

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