math16B_review_exer2

math16B_review_exer2 - Math 16B, Section 1 Sarason REVIEW...

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Math 16B, Section 1 Fall 2005 Sarason REVIEW EXERCISES 2 1. Perform the differentiations. (a) d dt (sin(ln t )) (b) d dt (ln(sin t )) (c) d dt (sec( e t )) (d) d dt (tan(sec t )) 2. Evaluate the integrals. (a) Z e 1 ln x x dx (b) Z π/ 2 0 x 2 cos x dx (c) Z π/ 2 0 cos 3 x sin x dx (d) Z π/ 2 0 cos 3 x dx 3. Perform the integration Z x x - 1 dx both by substitution and by integration by parts. Reconcile the two answers. 4. The hypotenuse of a right triangle has length 13 meters and one side has length 5 meters. Find the tangent of the angle adjacent to that side and the tangent of the angle opposite that side. 5. A surveyor measures the angle of elevation of the top of a building as seen from a spot on the ground at a distance of 100 feet from the building and finds it to be 1 . 25 radians. Given that sin 1 . 25 . 95 and cos 1 . 25 . 39, estimate the height of the building. 6. The minute hand on the clock of the Vergessen Memorial Tower is 7 feet long. What is the vertical speed in feet per minute of the tip of the minute hand at 12:15p.m.?
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math16B_review_exer2 - Math 16B, Section 1 Sarason REVIEW...

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