Hw 06 questions fall 2016 PDF

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Monday October 10, 2016...

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Math 2413

Homework Set 6

10 Points

Implicit Differentiation For problems 1 & 2 find y′ .

(

)

1. cos ( y ) + 9 x3 = y 2 + 1 e6 x 2. x 5 + 4 y 2 = 1 − e6 y − x

2

4

3

3. Find the equation of the tangent line to sin ( 8 xy) + x y = 0at (7, 0). Related Rates In order to receive any credit for problems 4 – 6 you MUST use Calculus techniques to find the answer. Any decimal work should include at least 4 decimal places. 4. An icicle in the shape of a perfect cone is forming in such a way that it is gaining 10 cm3 of volume every hour. At one point the icicle was measured and found to be 1.25 meters long and had a base radius of ¾ meters. When the icicle was only 40 cm long at what rate was the base radius changing? At what rate was the length changing at the same time? 5. A person is sitting on the ground holding a spool of string that is attached to a kite in the air that is a constant 80 feet above the ground and moving away from the person. At what rate is the angle that the string makes with the ground changing when 135 feet of string has been let out and string is coming off the spool at a rate of 0.2 ft/sec? For this problem assume that the spool is in fact resting on the ground. 6. Two boats start out 1000 miles apart with boat A directly to the west of boat B. At the same time both boats start moving with boat A traveling to the east at 45 mph while boat B travels north at 15 mph. Determine if the distance between the boats is increasing, decreasing or not changing at, (a) 13 hours (b) 20 hours (c) 32 hours Higher Order Derivatives For problems 7 – 10 compute the second derivative. 7. h ( t ) = 7 t10 − 9t 2 +

1 − 790t 8t 2

8. f ( x ) = sin (6 x + 7 ) + 4e x

(

3 9. y = ln z − 2 z

10. Compute g

( 3)

2 +3

x

) ( x ) for g (x ) = ln ( 2x 3 ) + e 6x − 2 cos ( 4x )...