Section MWF 12 1pm SR 117
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1 Math 1431 Section MWF 12 1pm SR 117 Dr. Melahat Almus COURSE WEBSITE: Visit my website regularly for announcements and course material! If you me, please mention your course (1431) in the subject line. Check your CASA account for quiz due dates; don t miss any quizzes. BUBBLE IN PS ID VERY CAREFULLY! If you make a bubbling mistake, your scantron will not be saved in the system and you will not get credit for it even if you turned it in. Bubble in Popper Number. DID YOU RESERVE A SEAT FOR TEST 2? REVIEW FOR TEST 2 is posted on course website! Be considerate of others in class. Respect your friends and do not distract anyone during the lecture. 1
2 Popper # Question# If 2 3 x y 5y 1, dy dx 12,? a) 4/7 b) -2/7 c) 7/5 d) -3/7 e) None 2
3 Chapter 3 Section 3.1 Related Rates You should know these formulas from Geometry: Volume of a sphere, cone, cylinder, prism, cube. Area of a circle, rectangle, triangle Surface area of a cube, right cylinder, prism. Pythagorean Theorem. Related Rates: Draw a picture. What do you know? What do you need to find? Write an equation involving the variables whose rates of change either are given or are to be determined. (This is an equation that relates the parts of the problem.) Implicitly differentiate both sides of the equation with respect to time. This FREEZES the problem. Solve for what you need. Example 1: Assume that oil spilled from a ruptured tanker spreads in a circular pattern whose radius increases at a constant rate of 2 ft/sec. How fast is the area of the spill increasing when the radius of the spill is 60 feet? 3
4
5 Example 2: Suppose a spherical balloon is inflated at the rate of 10 cubic centimeters per minute. How fast is the radius increasing when the radius is 5 centimeters? 4
6 Example 3: Water is pouring into an inverted cone shaped tank at the rate of 20 ft 3 /min. The tank is 10 ft. tall and has a radius of 4 ft. How fast is the height of the water rising when it is 5 ft deep? 5
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8 2 Example 4: A point moves along the curve y 4x x in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x =5? 6
9 Example 5: A 5 foot ladder, leaning against a wall, slips so that its base moves away from the wall at a rate of 2 ft/sec. How fast will the top of the ladder be moving down the wall when the base is 4 feet from the wall? 7
10 Example 6: A 6 foot man is walking towards a 25 foot lamp post at the rate of 10 feet per second. How fast is the length of his shadow changing when he is 20 feet from the lamp post? 8
11 Example 7: If a rocket is rising vertically at the rate of 1200 ft/sec when it is 4000 feet up, how fast is the camera-to-rocket distance changing at the instant? 3000 ft 9
12 Example 8: Using the same conditions for the rocket in #7, how fast must the camera elevation angle change at the instant to keep the rocket in sight? 3000 ft 10
13 Exercise: The altitude and base of a triangle is changing at a constant rate of 2 in/sec and 3 in/sec respectively. How fast is the area changing when base is 10 inches and altitude is twice the base? 11
14 Exercise: The length of a rectangle is increasing at a rate of 2 in/min while the width is decreasing at a rate of 3 in/min. How fast is the area changing when length is 20 and width is 5 inches? 12
Math 1431 DAY 14. Be considerate of others in class. Respect your friends and do not distract anyone during the lecture.
Math 1431 DAY 14 BUBBLE IN PS ID VERY CAREFULLY! If you make a bubbling mistake, your scantron will not be saved in the system and you will not get credit for it even if you turned it in. Be considerate
Math 1431 DAY 14. Be considerate of others in class. Respect your friends and do not distract anyone during the lecture.
Math 1431 DAY 14 BUBBLE IN PS ID VERY CAREFULLY! If you make a bubbling mistake, your scantron will not be saved in the system and you will not get credit for it even if you turned it in. Be considerate
Math 1431 DAY 16. Dr. Melahat Almus. OFFICE HOURS: MWF 11-11:30am, MW 1-2:15pm at 621 PGH
Math 1431 DAY 16 Dr. Melahat Almus almus@math.uh.edu OFFICE HOURS: MWF 11-11:30am, MW 1-:15pm at 61 PGH If you e-mail me, please mention your course (1431) in the subject line. Check your CASA account
Math Dr. Melahat Almus. OFFICE HOURS (610 PGH) MWF 9-9:45 am, 11-11:45am, OR by appointment.
Math 43 Dr. Melahat Almus almus@math.uh.edu http://www.math.uh.edu/~almus OFFICE HOURS (60 PGH) MWF 9-9:45 am, -:45am, OR by appointment. COURSE WEBSITE: http://www.math.uh.edu/~almus/43_fall5.html Visit
Section MWF 12 1pm SR 117
Math 1431 Section 1485 MWF 1 1pm SR 117 Dr. Melahat Almus almus@math.uh.edu http://www.math.uh.edu/~almus COURSE WEBSITE: http://www.math.uh.edu/~almus/1431_sp16.html Visit my website regularly for announcements
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4.6 Related Rates 8 b o lk0uct5ai FSHopfitcwkadr9ee MLBL1Cv.0 h ca5lrlx 8rzi8gThzt Zs9 2rJejsqeprTvCeVdy.w Solve each related rate problem.
-- g 52P0l33e 5Ktu3tlaY tswobfrtcwsawrkeq mlzlzcd.u 2 7AklGlf lrbiegkhjtbsa 9rlewsSeIr2vPeVdW.L 2 7Mza5dWeI gwbimtmhn bimnff0ieneistuet SCDallJcrulsuTsG.k Calculus 4.6 Related Rates 8 b230593 o lk0uct5ai
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