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Unformatted text preview: Practice Problems for Midterm 2 1)Differentiate f ( x ) = q 1 + p 1 + x . 2)Differentiate f ( x ) = sin(tan( p sin( x )). 3)Write f ( x ) = cos 3 ( 2ln( x ) x 3 +1 ) as a composition of 3 functions and then differentiate f ( x ). 4)Find y if sin( x + y ) = y 2 cos( x ). 5)Find y if ln( x 2 +1)+tan( xy ) 3 x 2 + e y = 2. 6)Show that the tangent to the elipse x 2 a 2 + y 2 b 2 = 1 at the point ( x ,y ) is x x a 2 + y y b 2 = 1. 7)Find the tangent line of y 2 ( y 2- 4) = x 2 ( x 2- 5) at the point (0 ,- 2). 8)A balloon is rising at a constant speed of 5 ft/s. A boy is cycling along a straight road at a speed of 15 ft/s. When he passes under the balloon, it is 45 ft above him. How fast is the distance between the boy and the balloon increasing 3 secons later? 9)The minute hand of a clock has length 8 cm and the hour hand has length 4 cm. How fast is the distance between the tips of the minute hand and the hour hand of a clock changing at 2:00 pm. 10)Find dx/dt where x 2 + y 2 = 25 and dy/dt = 4. 11)Explain why when x is close to 0 and positive we have that tan( x ) x/ 2. 12)Estimate (26) 2 / 3 . 13)The radius of a circular disk is measured to be 24 cm with a maximum error in measurement of .2cm....
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- Fall '08