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Part of 2017 CMI B.Sc. Entrance Exam

Problems(1)

CMI 2017 #1

Source: CMI 2017

4/26/2018
Answer the following questions :
(a) Evaluate   lim⁡x→0+(xxx−xx)~~\lim_{x\to 0^{+}} \Big(x^{x^x}-x^x\Big)
(b) Let A=2π9A=\frac{2\pi}{9}, i.e. 4040 degrees. Calculate the following 1+cos⁡A+cos⁡2A+cos⁡4A+cos⁡5A+cos⁡7A+cos⁡8A1+\cos A+\cos 2A+\cos 4A+\cos 5A+\cos 7A+\cos 8A (c) Find the number of solutions to ex=x2017+1e^x=\frac{x}{2017}+1
CMIChennai Mathematical InstituteB.Scmathematicscomputer science2017calculus