practice-sol2

# practice-sol2 - xy = 3 Diﬀerentiate to get xy dz dt xz dy...

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Math 1A Calculus Fall, 2004 Prof. Haiman Practice Exam for Midterm 2—Solutions 1. Diﬀerentiate e x (cos x + sin x ). 2 e x cos x 2. Diﬀerentiate ln( 873 sin x ). (cot x ) / 2 3. Find d 3 dx 3 ( x 3 ln x ). 11 + 6 ln x 4. Diﬀerentiate x (1 /x ) . x (1 /x ) x - 2 (1 - ln x ) 5. A table of values for f ( x ), g ( x ), f 0 ( x ) and g 0 ( x ) is given. If h ( x ) = f ( g ( x )), ﬁnd h 0 (1). x f ( x ) g ( x ) f 0 ( x ) g 0 ( x ) 1 3 2 1 7 2 1 4 5 2 3 3 1 3 1 h 0 (1) = f 0 ( g (1)) g 0 (1) = f 0 (2) g 0 (1) = 35 6. Find dy/dx if y = sin( x + y ). cos( x + y ) 1 - cos( x + y ) 7. If xyz = 6, dx/dt = 5 and dy/dt = 4, ﬁnd dz/dt when x = 1 and y = 2. Solve the given equation for z = 6 /
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Unformatted text preview: ( xy ) = 3. Diﬀerentiate to get xy dz dt + xz dy dt + yz dx dt = 0, so 2 dz dt + 12 + 30 = 0, and dz/dt =-21. 8. The radius of a circular disk is measured to be 20cm with a possible error of . 2cm. Estimate the possible error in computing the area of the disk. A = πr 2 , dA = 2 πrdr = 2 π 20( . 2) = 8 π ≈ 25cm 2 1...
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