Exercise 10.1 Let1kk a k . Write an M-file that 10–Series10.10a) plots (you can use a regular plot, instead of a semilog plot) the first 100 values of thesequence as individual pointsb) based on the numeric values generated makes an estimate of the limit of the sequencec) uses the Symbolic Toolbox to find the exact limit.Publish your M-file. The results of a), b), and c) should appear as separate output fromdifferent cells in the file. Don’t forget to include your name at the top. Exercise 10.3 Investigate which if any of the following sequences have limits. Provideall possible justifications for your answer using a variety of Matlab computations andgraphs. Present your work in the form of a published M-file with appropriate comments:a)sin( ) k a k b)(sin( ))kkb k c)1 1 1 1 ln2 3 kc kExercise 10.7 Investigate the convergence or divergence of each of the following series.You should use numerical and/or symbolic computations to arrive at your conclusions. 10–Series10.11To the extent possible you should confirm your answers using the theory covered in thecourse. Present the response to each part as a separate published M-file.a)11( 1)2kkk b)11! k k(The quantityk !can be entered in Matlab as factorial(k).)c)1sin( )kkkd)21sin( )kkke)11( 1)( 2)