Practice test 3

# Practice test 3 - removed[VOLUME when the radius is 9 cm 3...

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PRACTICE TEST 3 1. Find dy dx [by implicit differentiation]: 3 3 2 3 x y xy + = 2. Use implicit differentiation to find all points on the graph of ( 4 2 1 y y x x = - at which the tangent line is vertical. 3. Use logarithmic differentiation to find dy dx : 3 2 1 y x x = + 4. Find dy dx : a) ( 3 ln 2 y x x = b) ( cos ln y x = c) 2 2 1 x x y x = - [Use the quotient rule] d) 2 tan y x = 5. Determine whether the function ( 2 sin f x x x = + is one-to-one by examining the sign of ( f x . 6. Find the differential dy if 1 y x x = - 7. Find dy dx : a) 1 sec x y e x - = b) ( 1 3 tan y x - = 8. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min. At what rate must air be
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Unformatted text preview: removed [VOLUME] when the radius is 9 cm? 3 4 3 V r π = 9. Use an appropriate linear approximation to estimate the value of 80.9 10. A rocket, rising vertically, is tracked by a radar station that is on the ground 5 miles from the launchpad. How fast is the rocket rising when it is 4 miles high and its distance from the radar station is increasing at a rate of 2000 mph? MAKE A SKETCH 11. Show that for any constants A and k , the function kt y Ae = satisfies the equation dy ky dt = 12. Find dy dx : log x y e =...
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