NAME______________________ AP CALCULUS DIFFERENTIAL CALCULUS II TEST AFULL SOLUTION: Answer each question on the LEGAL SIZEpaper provided with COMPLETE STATEMENTSwhen required. 1)(4A, 1C) Let ( )()x ttt=++281lnrepresent the position of a particle in meters on the x–axis with t≥0seconds. Find the velocity of the particle when the acceleration is zero. 2)Evaluate the following limits. Show all your work for full marks. a)(2K) limcostanxxxx→−021b)(2K) limarctanarcsinsinxxxx→−034c)(3K) limxxxxxxxxx→−+−+−+−+143243241216722213)Consider the function()yx=cosarcsin2, x∈ −11,. a)(3K, 1C) Show that ()yx=cosarcsin2can be simplified to yx=−122. b)(1K) Find dydxin simplest terms. 4)(3K, 1C) Let ()fxbe a continuous differentiable function such that ( )f310=and ()′≥fx4for 37≤≤x. How small can ()f7possibly be? 5)(4K, 1C) Let()g x
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