MATLAB Exercise 7 School of Mathematical Sciences Xiamen University http∥gdjpkc.xmu.edu.cr 2)C=[a1-2a2+a3,a2-2a3+a4…,an-2-2an1+an] Help Select Matlab Help in the toolbar, then select Index and input diff to see its different 8. Calculate the following calculus )∫d 1 2) x x+1 (x2y+1) l) Help Select Matlab Help in the toolbar, then select Index and input int to know the usage of this function, for example: int(f,x, -inf, inf) 9. Let f=x +1, compare it with the results of int( diff(f)and diff( int(f), respectively 10. Compute the following summations ∑k2 k ∑ 11. Evaluate Taylor series expansion to to the first 15 iter 2)f(x)=e-at point-I to the first 9 items 3)f(x)=e- the first 5 items of Taylor series expansion responding to x 12. *Compare the result.(cosx+2x)dr with sinl a+b),,(a+b) 2(b-a)when b equals to a+10, a+5z, a+T, a+1/2T, a+1/64, a+1/2567,respectively.What conclusion you may reach? 13.*Examine integral mean-value theorem, that is for any f(eCLa, b, there is a e(a, b) such that/(xkr=f(5)(b-a). For example, try to find out the 5E(0,1),such (x+1)(2+1)2 Ex7-2MATLAB Exercise 7  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Ex7­2  2) 1 2 3 2 3 4 2 1  [ 2 , 2 ,..., 2 ] C n n n  a a a a a a a a a = - + - + - - - + . Help Select Matlab Help in the toolbar, then select Index and input diff to see its different  usage.  8.  Calculate the following calculus  1) 1 1 dx  x + Ú 2) 1  0  1 1 dx  x + Ú 3) 0  1 1 t  dx  x + Ú 4) 2 sin  ( 1) y  dx  x y +• -• + Ú 5) 2 sin  ( 1) y  dxdy x y +• +• -• -• + Ú Ú . Help Select Matlab Help in the toolbar, then select Index and input int to know the usage of this function , for example: int(f,x,­inf,inf) 9.  Let  2  f = x +1, compare it with the results of int(diff(f)) and diff(int(f)), respectively.  10.  Compute the following summations  1) 3  1 n  k k  = 2) 1  2  1 1 k k • = -  3) 2  2  1 1 k k • = -  4) 2  1 k k k x •  = 11.  Evaluate Taylor series expansions of  1) 2  ( ) x f x = e at point 0 to the first 15 items; 2) 2  ( ) x f x = e at point ­1 to the first 9 items;  3) 2  ( ) xy f x = e the first 5 items of Taylor series expansion responding to x.  12.  *Compare the result  (cos 2 ) b  a  x + x dx Ú with  ( ) sin 2 ( ) 2 2 a b a b  b a Ê Ê + ˆ + ˆ Á ˜ + - Á ˜ Ë Ë ¯ ¯ when b equals to a +10p ,  a + 5p , a +p ,  a+1/2p ,  a +1 64p ,  a +1 256p ,  respectively.  What  conclusion you may reach? 13.  *Examine integral mean­value theorem, that is for any f (x)ŒC[a,b], there is ax Œ(a,b) ,  such that  ( ) ( )( ) b  a  f x dx = f x b - a Ú .  For example,  try to find out  the x Œ(0,1) ,  such  that  1 2 2 0 1 1  ( 1) ( 1) dx  x x = + + Ú