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` - 2005 ex e exp x sh x = (ex - e-x)/2, ch x = (ex + e-x)/2, th x = sh x/ch x x0, 0, 001 x (-1)n(2n4 - 1).

n6 + 5n + 6 n=1 (-1)n(2n4 - 1) un =.

n6 + 5n + 6 2n4 - 1 2n4 2 1 |un| = < =.

n6 + 5n + 6 n6 n2 n2 n=1 1 1 dx = 1 dx x2 x2 1 1 1 n2 n=1 2 n2 n=1 |un| n=1 (-1)n(2n4 - 1) n6 + 5n + 6 n=1 2n4 - 1 1 2 - 1/n4 |un| |un| = = lim = 2, n6 + 5n + 6 n2 1 + 5/n5 + 6/n6 n 1/n2 2n4 - 1 1 n6 + 5n + 6 n2 n=1 n=1 (-1)n(n5 + n3 + 5) n6 + n2 - 1 n=1 (-1)n(n5 + n3 + 5) = un n6 + n2 - 1 n5 + n3 + 5 n5 n5 1 1 |un| = > = .

n6 + n2 - 1 n6 + n2 2n6 2 n 1 n n=1 1 1 1 dx = ln x = dx x x n 1 n=1 1 1 n5 + n3 + 5 |un| = n6 + n2 - 1 n=1 n=1 n5 + n3 + 5 1 |un| = n, n6 + n2 - 1 n 1 |un| n n=1 n=1 |un| n=1 x5 + x3 + 5 (x) =, (n) = |un|.

x6 + x2 - 1 (5x4 + 3x2)(x6 + x2 - 1) - (6x5 + 2x)(x5 + x3 + 5) (x) = = (x6 + x2 - 1)2 -x10 - 3x6(x2 - 1) - 30x5 - 4x4 - 3x2 - 10x =.

(x6 + x2 - 1)2 (x) < 0 x 1 (x) [1, ) |un| n5 + n3 + 5 lim |un| = lim = 0.

n n n6 + n2 - 1 (-1)n(n5 + n3 + 5) n6 + n2 - 1 n=1 n + 1 arctg.

2n n=0 arctg((n + 1)/2n) = un arctg x x x 0 un+1 (n + 2)2n 1 lim = lim = < 1.

n un n 2n+1(n + 1) 2 arctgn+1 2n n=0 2n3 + 3 (-1)n ln.

5n3 + 7 n=1 n 2n3 + 3 2 |un| = ln - ln = 0 lim un = 0.

n 5n3 + 7 5 2n3 + 3 (-1)n ln.

5n3 + 7 n=1 (-1)n+1 (x + 5)n.

2n n=0 (-1)n+1 un(x) = (x + 5)n 2n |x + 5|n |un(x)| =, 2n |un+1(x)| |x + 5|n+12n |x + 5| lim = lim = = q(x).

n n |un(x)| 2n+1|x + 5|n 2 |un(x)| q(x) < 1 n=0 q(x) > 1 q(x) = 1 |un(x)| |x + 5| < 2 n=0 |x+5| > 2 |x+5| < 2 |x+5| > 2 (-7, -3) x1 = -7 x2 = -3 q(x) = 1 un(x1) = (-1)2n+1 = -1, un(x1) 0 n, un(x1) n=0 un(x2) = (-1)n+1 n=0 n=0 Sn(x1) = -n - 1 - n -1, n Sn(x2) = 0, n Sn(x2) (-7, -3) 3n.

(n + 1)(2 - x)n n=3n 3n un(x) =, |un(x)| =, (n + 1)(2 - x)n (n + 1)|2 - x|n |un+1(x)| (n + 1)3n+1|x - 2|n lim = lim = = q(x).

n n |un(x)| (n + 2)3n|x - 2|n+1 |x - 2| q(x) < |x - 2| > (-, -1) (5, ) (-1, 5) q(x) > q(x) = 1 x1 = -1 x2 = x1 = - un(-1) = x2 = n + n=0 n= (-1)n un(5) = n + n=0 n= (-, -1) [5, ), x = f(x) = tg x f(n)(0) f(x) = xn f(n)(0) n n! n= (f(0)(0) = f(x)) f(0) = tg 0 = x = f (x) = 1/ cos2 x, f (0) = 1;

f (x) = 2 cos-3 x sin x, f (0) = 0;

f (x) = 2 cos-2 x + 6 cos-4 x sin2 x, f (0) = 2;

fIV (x) = 16 cos-3 x sin x + 24 cos-5 x sin3 x, fIV (0) = 0;

fV (x) = 8 cos-2 x (2 + 15 tg4 x + 15 tg2 x), fV (0) = 16.

tg x = x + x3/3 + 2x5/15 +...

f(x) = arctg (sinx) f(0) = 0;

cos x f (x) =, f (0) = 1;

1 + sin2 x - sin x(1 + sin2 x) - cos x 2 sin x cos x f (x) = = (1 + sin2 x)sin2 x - = sin x , f (0) = 0.

(sin2 x + 1)sin2 x - 3 7 - sin2 x = (x) = (x) (sin2 x + 1)2 (sin2 x + 1)f (x) = cos x (x) + sin x sin 2x(x), f (0) = -3;

fIV (x) = (x)(- sin x +2 cos x sin 2x + + sin x cos 2x) + sin x sin 2x (x), fIV (0) = 0;

fV (x) = - cos x (x) + 6 cos x cos 2x (x) + + sin x [ (x) sin 2x + 2 (x)(3 cos2 x + 2 cos 2x) - 3 sin 2x (x)], fV (0) = 3 + 42 = 45.

arctg (sin x) = x - x3/2 + 3x5/8 +...

x f(x) = e3-x + 5x, x0 = 2.

x - x0 = x - 2 = -t x = -t + e3-x + 5x = e1+t - 5t + 10 = t2 tn = e(1 + t + +... + +...) - 5t + 10 = 2 n! tn = e + 10 + (e - 5)t + e = n! n= (-1)n(x - 2)n = e + 10 + (5 - e)(x - 2) + e.

n! n= et t (-, +). x = -t + (-1)n(x - 2)n e3-x + 5x = e + 10 + (5 - e)(x - 2) + e n! n=x (-, +).

f(x) = (x2 + 2x - 3)-1, x0 = 1 1 1 1 f(x) = = - = x2 + 2x - 3 4 x - 1 4 x + -1 1 1 x = - (1 - x)-1 + (3 + x)-1 = - (1 - x)-1 + 1 +.

4 4 3 (1-x)-1 (1+x/3)- (1 + t) = -1, t = -x t = x/-1 n 1 x (-1)n x (1 - x)-1 = xn, 1 + =.

3 3 3 n=0 n= (-1, 1) (-3, 3) (1 - x)-1 (1 + x/3)- -1/ xn (-1)n (-1)n+1 - 3n+ f(x) = - 1 + = xn, 4 3n+1 n=0 4 3n+n= (-1, 1) (-1)n+1-3n+ f(x) = xn x (-1, 1).

43n+n= f(x) = ln(-x2 + 2x + 3), x0 = 2.

x - 2 = t;

(-1)n-1xn f(x) = ln(1 + x) = n n=f(x) = ln [-(t + 2)2 + 2(t + 2) + 3] = ln [-(t2 + 2t - 3)] = t t = ln 3(1 - t) 1 + = ln 3 + ln (1 - t) + ln 1 + = 3 tn (-1)n-1tn = ln 3 - +, t = x - 2.

n n3n n=1 n= ln (1 - t) - tn/n n= (-1)n-1tn J1 = [-1, 1) ln (1+t/3) n3n n= J2 = (-3, 3] J -1 t < 1 t = x - -1 x - 2 < 1 1 x < x, 3n + (-1)n ln (-x2 + 2x + 3) = ln 3 - (x - 2)n, n3n n= [1, 3).

e-x dx 0, tn f(t) = et = n! n= 2 (-1)nx2n e-x =.

n! n= 2 (-1)n x2n+1 (-1)n e-x dx = =.

n! 2n + 1 0 n=0 n!(2n + 1) n= n (-1)5 |a5| = = < 0, 001.

5! ( 2 5 + 1) 120 1 1 1 S4 = 1 - + - + 0, 747.

3 10 42 e-x dx 0, 747.

x - xy = 0, y y(0) = 1, y (0) = 0.

y(n)(0) y = xn, y(0) = 1, y (0) = 0, n! n= y(n)(0), n y = xy y (0) = 0, y = y + xy y (0) = y(0) = 1, yIV = 2y + xy yIV (0) = 2y (0) = 0, y(n+3) = (n + 1)y(n) + xy(n+1) y(n+3)(0) = (n + 1)y(n)(0).

y (n + 3) n y (0) = y (0) = 3m + 1 3m + 2 m = 0, 1, 2..., x = yV I(0) = 4 y (0) = 4 1, yIX(0) = 7 yV I(0) = 7 4 1,...

y(3m)(0) = 1 4 ... [3(m - 1) + 1], m = 1, 2,...

1 4 ... (1 + 3(m - 1)) y(x) = 1 + x3m (3m)! m= y(x) = anxn n=a0 = y(0) = 1, a1 = y (0) = anxn n= y y y = nanx(n-1), y = n(n - 1)anxn-2.

n=1 n= n(n - 1)anxn-2 - anxn+1 = 0.



n=2 n=n m m - 2 = n + m = n + 3, m - 1 = n + m(m - 1)amxm-2 = 2a2 + (n + 3)(n + 2)an+3xn+1.

m=2 n= 2a2 + [(n + 3)(n + 2)an+3 - an]xn+1 0.

n= g(x) cn+1 = (n + 3)(n + 2)an+3 - an = g(n)(0)/n! = 0 n > 0 c0 = 2a2 = g(0) = an a2 = 0 an+3 = (n + 3)(n + 2) a1 = 0 a2 = a3m+1 = a3m+2 = 0 m = 0, 1, 2,...

a3(m-1) aa3m = = = 3m(3m - 1) 3m(3m - 1)(3m - 3)(3m - 4) ... 3 1 4 ... (1 + 3(m - 1)) = a0, a0 = 1.

(3m)! 1 4 ... (1 + 3(m - 1)) y(x) = 1 + x3m.

(3m)! m=f(t) 0 1 2 3 t - [0, 3] [0, 2] -1 f(t) = -1 t [0, 2] [2, 3] l (2, -1) (3, 0). (x1, y1) y - y1 x - x(x2, y2) =.

y2 - y1 x2 - xx = t, x1 = 2, y1 = -1, x2 = 3, y2 = 0 y = t - l t, y.

-1, 0 t 2, f(t) = t - 3, 2 t 3.

a+ an cos nt + bn sin nt, n= = 2/T, T [a, b], f(t), an, bn f(t) b an = f(t) cos nt dt, n = 0, 1, 2,...

T a b bn = f(t) sin nt dt, n = 1, 2, 3,...

T a [ 0, 3 ], a = 0, b = 3, T = b - a = 2 2 2 t2 a0 = (-1)dt + (t - 3)dt = -2 + - 3t = -.

3 3 2 0 2 2 2nt 2nt 2 3 2nt an = - cos dt + (t - 3) cos dt = - sin dt + 3 3 3 3 2n 0 3 2nt 3 9 2nt 3 3 4n + (t - 3) sin + cos = - 1 - cos.

2n 3 (2n)2 3 22n2 2 2 2 2nt 2nt 2 3 2nt bn = - sin dt + (t - 3) sin dt = cos dt 3 3 3 3 2n 0 3 2nt 3 9 2nt 3 1 3 4n - (t - 3) cos + sin = - - sin.

2n 3 (2n)2 3 n 22n2 2 f(t) T = t = 3n, S(3n) = -1/2 n = 0, 1, 2,..., S(t) S(t) S(t) -6 -5 -4 -3 -2 -1 1 2 3 4 5 t - 5 3 4n 2nt f(t) = - + 1 - cos cos 6 22n2 3 n=1 3 4n 2nt - + sin sin, t (0, 3);

n 22n2 3 S(t) = f(t), t = 3n; S(3n) = - n = 0, 1, 2,...

[ -3, 0 ].

f(t) [-3, 3] T = 6, T/.

n n 4 f(t) sin ntdt, n = 1, 2,...

f(t) = b sin nt, b = T n=n b 2 n = 2 sin ntdt + (t - 3) sin ntdt = 2 3 cos nt b - 3 3 3 3 n 0 3 nt 3 9 nt 3 2 3 2n - (t - 3) cos + sin = - - sin.

n 3 (n)2 3 n 42n2 2 S(t) = f(t) t = 6k, f(t) f(t) S(6k) = 0 k = 0, 1, 2,...

S(t) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 t - 2 3 2n nt f(t) = - + sin sin t (0, 3], n 42n2 3 n= S(t) = f(t) t = (6k) S(6k) = 0 k = 0, 1, 2,...

[ -3, 0 ].

f(t) [-3, 3] T = 6, T/0.

f(t) = + n cos nt, n = f(t) cos ntdt, n = 0, 1, 2,...

2 T n= n :

2 2 0 = - dt + (t - 3)dt = -, 3 0 2 2 nt nt 6 2n n = - cos dt + (t - 3) cos dt = (-1)n - cos.

3 3 3 2n2 0 S(t) =f(t) t f(t) f(t) S(t) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 t - 5 6 2n nt f(t) = - + (-1)n - cos cos t [0, 3] 6 2n2 3 n= S(t) =f(t) t f(t) b.

-f(t) = cn eint, cn = T f(t) e-intdt, = 2/T.

a n= a = 0, b = 3, T = 3, = 2/3, c0 = 3-1 f(t)dt = a0/2 = -5/6, 2 3i - cn = 3-1 e-intdt + (t - 3)e-intdt = 3-1 - e-int + 2n 0 3i 3i i + (t - 3)e-int - e-int = + 1 - e-2ni = 2n 2n 2n 42n3 4n i 3 4n = 1 - cos + 1 + sin.

42n2 3 2n 2n cn an, bn 2-1(an - ibn), n 0, cn = 2-1(a-n + ib-n), n < 0.

T = 3, t = 3n, S(3n) = -1/2 n = 0, 1, 2,...

S(t) -6 -5 -4 -3 -2 -1 1 2 3 4 5 t - 5 3 4n f(t) = - + 1 - cos + 6 42n2 n=-, n =i 3 4n + 1 + sin ei2nt/3 t (0, 3) 2n 2n S(t) = f(t), t = 3n; S(3n) = - n = 0, 1, 2,...

F () f(t) f(t) = e-3|t| f(t) F () = (2)-1/2 f(t) e-itdt.

1 F () = e-3|t|e-itdt = e(3-i)tdt + e-(3+i)tdt = 2 - 1 1 1 2 = + = .

2 - i 3 + i 9 + f(t) F () f(t) = (2)-1/2 F () eitd, F () f(t), eit d = e-3|t|.

9 + 2 t 1, t [-1, 1], f(t) = 0, t [-1, 1].

/ 1 1 e-it 1 ei - e-i 2 sin F () = e-itdt = = =.

2 2 -i i --, t (-1, 1), sin eitd = /2, t = 1, 0, t [-1, 1].

/ / f(t) (2n + 1)! (-1)nn n! 2n 3n + nn=1 n= 1 1 tg n + 1 n (n + 1) ln (n + 1) n=1 n= 2n + 3n+1 (-1)n-1(n + n) 5n (n + 1) (n + 3) n=1 n= 2n+1(n3 + 1) 1 1 + cos 1 + (2n + 1)! n nn=1 n= (2n + 2)! 3n (-1)n sin n! (n + 1) 2n n2 - 2n + n=1 n= 1 arcctg n2 + (n + 3) ln3(n + 3) n=1 n= (3n + 1)! arctg (1/(n + 1)) n + n! n2 + n=1 n= 1 (-1)n(3n + n) n2 sin n2 + 1 4n + n=1 n= sin(3/n) 4n + n2 + 1/n 2n +n n=1 n= (-1)n(2n + 1) n! n (n + 1) (2n)! 5n n=1 n= 3n + 5 2 5 ... (3n - 1) n3 + 6 4n+2 (n - 5)! n=1 n= 4 (-1)n arccos n2 + 1 (n - 1) ln (n - 1) n=1 n= 1 1 3 ... (2n - 1) sin2 + 2 n2 3n (n + 1)! n=1 n= (-1)n en + e-n (n n=1 n=4 - 2) ln3/2(n - 2) (n!)2 (-1)n 2n (3n + 1) (2n)! n4 + n n=1 n= (-1)n-1 n3 1 - n arctg n4 + 2n + 1 n + n=1 n= n2 + 5 1 4 ... (3n - 2) 3n + n3 7 9 ... (2n + 5) n=1 n= (-1)n ln n n2 + arctg n 3 - nn=2 n= (3n + 2)! 2n + (-1)ncos 10n n2 3n + n=1 n= 3n + n2 ln 1 + 5n + n n n - n=1 n= (-1)n 3n + ln 3n - 3n n=3 n= (2n)! n 5n -5n + 1 6n + nn=1 n= sin 3n ( n2 + n - n) 3n + n n=1 n= (n!)2 2 ln 1 + + 2n n nn=1 n= (-1)n 2n + ln n + n ln n n + n=1 n= 10n 2 n! 3n + 4n (2n)! 5n n=1 n= 5 2n + (-1)n cos (-1)n 2n n2 + 9n + n=1 n= 5n 4 ln3/2 1 + + (2n)! n2 n n2 + n=1 n= n + n n 3n - (-1)n arcsin n3 + n2 - 1 6n + n=1 n= 2n (3n + 1)! 2n + 3 32n+n=1 n= 5n + n3 cos n (3n)! n + n=1 n= arctg 2n n + 1 1 - cos 3n + 5 n n=1 n= 1 n + (-1)n n2 + sin n ln (n + 4) n=1 n= n2 + 4n4 3 7 ... (4n - 1) en +1 5n (n + 3)! n=1 n= 3n - 1 ln (-1)narcsin 5n + 2 n + n=1 n= 4n n2 + 5 3n +n - 2n (2n - 1)! 76n+n=1 n= n! (2n + 1)! (-1)n ln (1 + n)sin (3n)! n n=0 n= 4n + cos n ln (1 + n/(n2 + 1)) 5n + n2 n + n=1 n= 5 1 4 ... (3n - 2) ctg n 2n+1 n! n=1 n= (-1)n ln 1 + 5n n ln n lnln n 3n + 2n n=7 n= n (-1)2n+ n e-n+n2 + n=1 n= 1 3 5 ... (2n + 1) 1 - cos n 2 5 ... (3n - 1) n=1 n= 2n - 5 (n + 3)! (2n + 3)! (-1)n ln 2n + 3 (3n - 2)! n=3 n= n + 1 2n + sin 3n + tg (1/n) n3 + 2n n=1 n= 2n 4 8 ... 4n arccos ln 2n + 1 3 8 ... (5n - 2) n=1 n= 3n + 4n+ (-1)n [(1 + 1/n)10 - 1] 2n +n=1 n= 3n (2n - 1)! 2n n! (3n - 1)! 3n + nn=1 n= (-1)n n n arctg 1 + (n + 1) n + 1 n2 + n=1 n= 6n (n2 - 1) 2sin (1/n) (2n + 1)! n=1 n= (-1)n 2n + 5n 3n + 6n+n3 + n + n=3 n= 2n + 3 2n (-1)n ln 2n + 1 (3n)! n=1 n= n (-1)n arctg 3n + nn ln3/4n n=1 n= 1 tg (-1)n cos n n 6n n=1 n= 5n (n + 1)! n3 + 2n (2n)! 7n + n2 + n=0 n= 1 1 n2 + cos (-1)n ln n n n2 + n=1 n= 4n + n n (2n + 1)! 5n - 1 4n-n=1 n= 1 1 (-1)n- arctg n - 1 n - 1 ln (1 + n) n=2 n= 6n + ln n (3n - 1)! 2n 3n (n + 3)! n=2 n= n 3n sin (n + 2)! 4n n5 + n=1 n= n + 2 5 2n + n (-1)n n + 4 3n+n=1 n= 2 (-1)n-1 (x + 1)2n+ (x + 1)n 3n.





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n + 2 n n=n= (-1)n (2x - 3)n 5n2 +.

(x + 5)2n.

32n 2n n=n= n3 + 1 (-1)n-1 (3x - 2)2n..

3n (x - 2)n 2n + n n=0 n= (n + 1)5 x2n (2x + 5)n tg.

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3n 3n nn=n= (x - 2)n..

4n + n2 (x - 5)2n+1 (2n + 7) n=0 n= 2n + (2x - 5)n.

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(n + 1)5 x2n (n + 4) ln (n + 4) n=n= (3x + 2)2n (3n - 2) (x - 3)2n.

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(2n + 1) 5n (n + 1)2 2n+n=n= 1..

n ln(n + 2) (x - 3)2n 9n (x - 1)2n n n=1 n= n2 (2x - 3)n (3x - 1)2n..

(n4 + 1)2 n 9n n=0 n= 3n2 + 4n.

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2n n2 (x + 2)n n=2n (x - 1)n n= n2n.

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(x - 1)4n n (x + 3)2n n=n= 4n (2x + 1)2n n2 +.

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n 5n (2x + 3)n n=n= (3x - 1)2n+3n + n.

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5n (x + 1)2n n=n= 4n2 + (x - 7)2n-.

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(3n + 7) (x + 3)n (2n2 - 4n) 5n n=n= 3n (x + 5)2n-..

(5n - 8)3 (x - 2)3n 4n (2n + 3) n=1 n= f(x) = ln(5 + e-2x). f(x) = 1 + x arctg(x + 1) f(x) = arcctg(2 + 3x)- f(x) = ln cos 3x f(x) = exp (arctg 3x).

f(x) = exp (arcsin 3x).

f(x) = exp (x2 + 4x + 7) f(x) = (cos 3x)-1.

f(x) = exp (5 - x)-1.

f(x) = ln (1 - sin x)- f(x) = (1 + ctg(x + 1))- f(x) = x sin(1 + 2x). f(x) = ex cos-1 2x.

x f(x) = e2x + 3.

f(x) = exp (1 + sin ) f(x) = ln(3 - sin 2x) f(x) = arctg e-3x.

f(x) = exp (1 + sin x) f(x) = x tg(x + 1).

f(x) = exp (tg 3x).

f(x) = arctg(1 - 2x) f(x) = 3 + 5x - x f(x) = 1 + cos x.

f(x) = x ctg(3 - x).

f(x) = arctg(2 + e-x) f(x) = 1 + arctg 2x f(x) = sin3(1 + x).

f(x) = ln2(1 - 5x).

f(x) = ln cos(1 - 3x) f(x) = 2 + 3x + x x f(x) = sin 3x, x0 = ;

f(x) = xe3+x, x0 = 1.

f(x) = e2+3x, x0 = 2;

f(x) = 6 sin x3 + x2(6 - x4), x0 = 0.

f(x) = ln(6 + 3x), x0 = -1;

f(x) = 2 - 3(x5 - x) + 3 cos x2, x0 = 0.

f(x) = 5(2 - x)-1/3, x0 = 1;

f(x) = x2 cos(x + 1), x0 = -1.

f(x) = cos(x/4), x0 = ;

f(x) = x2(1 + x)-2, x0 = 0.

f(x) = 23(x+1), x0 = -2;

f(x) = x(x + 2)-1, x0 = 1.

f(x) = ex -4x, x0 = 2;

f(x) = 1 + x2 - ln(2 - x), x0 = 1.

f(x) = (4 - 3x)-1, x0 = -1;

f(x) = (x + 2)(ex - 1), x0 = 0.

f(x) = (5 - 2x)1/3, x0 = 2;

f(x) = x sin(x + 1), x0 = -1.

f(x) = (x2 - 3x + 2)-1, x0 = 0;

f(x) = xe2x, x0 = 1.

f(x) = ln(2 - 5x), x0 = -3;

f(x) = sh2x, x0 = 1.

f(x) = (7 + 3x)-1/4, x0 = -1;

f(x) = ch3x, x0 = 2.

f(x) = ex -6x+7, x0 = 3;

f(x) = x(x2 - 2x + 5)-1, x0 = 1.

f(x) = (5 + x2)-1/2, x0 = 0;

f(x) = x2ex, x0 = 1.

f(x) = (2x - 5)-1, x0 = -3;

f(x) = x + 2 + xex, x0 = 1.

f(x) = cos(x/3), x0 = -3/2;

f(x) = xln(1 + 3x), x0 = 1.

f(x) = e-3(x +5), x0 = 0;

f(x) = x(x + 3)-1, x0 = 1.

f(x) = x3cos23x, x0 = 0;

f(x) = (x + 1)(x - 2)-1, x0 = 1.

f(x) = ex + x + 3, x0 = 2;

f(x) = (1 + x)ln(3 + x), x0 = -2.

f(x) = x2 + 3 + 1/x, x0 = 1;

f(x) = ch2x, x0 = -1.

f(x) = ln(x2 + 6x + 5), x0 = 0;

f(x) = xe1-x, x0 = 1.

f(x) = e2-x + 3x, x0 = 4;

f(x) = (7 - 2x)(x2 - x - 2)-1, x0 = 0.

f(x) = x2 + cos 2x, x0 = -;

f(x) = xln(4 + 3x), x0 = -1.

f(x) = (x2 + x)-1, x0 = -2;

f(x) = (2x + 3)(ex - 1), x0 = 0.

f(x) = x2e-6x, x0 = 0;

f(x) = x3 + ln(2 - x), x0 = 1.

f(x) = x2 cos(x3 + /4), x0 = 0;

f(x) = (x2 - 3x + 2)-1, x0 = -3.

f(x) = (2 + 7x5)-1/2, x0 = 0;

f(x) = shx, x0 = 2.

f(x) = (4x)1/3, x0 = -1;

f(x) = x2 + sin(1 - x), x0 = 1.

f(x) = sin(x2 + /4), x0 = 0;

f(x) = xln(3 + x), x0 = -1.

f(x) = (2x + 3)-2/3, x0 = -2;

f(x) = chx, x0 = 1.

0, 0,1 ln(1 + 2x) dx.

dx.

x 64 + x0,0,ln(1 + x/2) 1 - e-x/ dx dx x x 1,5 0, 1 81 + x4dx. e-6x dx.

0 0,2 0, cos(25x2)dx sin(100x2)dx 0 0,0,1 - e-x sin(5x/2)2dx.

dx.

x 0,2 e-2x dx dx 16 + x0 0,5 0, cos(4x2)dx. e-3x /4dx 0 0,2 0, sin(25x2)dx sin(4x2)dx.

0 0,2 0, e-3x dx. cos(100x2)dx 0 1,5 dx.

dx 256 + x27 + x0,ln(1 + x/5) dx. dx x 1 + x0 0,2,1 - e-2x dx dx.

x 625 + x0,1 dx. dx 4 1 + x4 8 + x0 1 0, cos x2dx e-3x /25dx.

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