Math 155a_Exam on Equations, Implicit Differentiation, Linear Approximation, Absolute Maxima and Min

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MATH 155A FALL 13PRACTICE MIDTERM 2.Question 1. Findy0.(a)y=1x-15x3.(b)y=tanx1 + cosx.(c)y=x21+πcosx.(d)y=1sin(x-sinx).(e)y= sin2(cos(psin(πx)).Question 2. Find an equation for the tangent line and normal line to the curve at the givenpoint.(a)y= (1 + 2x)2,(1,9).(b)y=xx+ 1,(4,0.4).(c)x2+ 2xy-y2+x= 2,(1,2).Question 3. An object of massmis shot straight upward from the ground with initial velocityv0. Assuming that there is no air resistance, the heighthof the object, measured with respectto the ground level, is given as a function of time, byh(t) =v0t-12gt2,wheretis the time, andgis the value of the gravitational acceleration.Show that themaximum height of the object ishmax=12v20g.Suppose that gravity in the planet Krypton is such that its gravitational acceleration is twicethat of Earth’s. How much faster would the object have to be shot in order to reach the sameheight?Question 4. Findy00by implicit differentiation.(a)x3+y3= 1.1
2MATH 155A FALL 13(b)x+y= 1.Question 5. Two sides of a triangle have lengths 12m and 15m. The angle between them is
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