NAME________________________ AP CALCULUS DIFFERENTIAL CALCULUS II TEST BFULL SOLUTION: Answer each question on the LEGAL SIZEpaper provided with COMPLETE STATEMENTSwhen required. 1)Evaluate the following limits. Show all your work for full marks. a)(2K) limxxxx→−−−432231144b)(2K) limlncosxxxe→−++−111πc)(2K) ()limarctan arcsinsinxxx→0622)Consider the functionyx=sinarccos2, x∈−11,. a)(3K, 1C) Show that =sinarccos2can be simplified to x=−212. b)(2K) Find dydxin simplest terms. 3)(3K, 1C) Let fxbe a continuous differentiable function such that ( )f515=and ()′≤2 for 59≤≤x. How large can f9 possibly be? 4)(4K, 1C) Letgxbe the inverse function to()xxx=+ +−531. Find the equation of the tangent line to()at the point,. 5)The air pressurePhat a height of hmeters above sea level is modeled by the formula () ()eh=−10130 000125..kilopascals (kPa). An instrument box carrying a device for measuring pressure is dropped into the ocean from a plane and falls in such a way that after
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