РГР (2 семестр)

.r4=(1nx)

In in.

X 78

sin

6

7x ·ln 3 4x

;y6

=1/sin

67

[J3x+4/(x

8

9

·;y5 =

~

cosx )]

tgn 5x

·

2.

x =31 /(21 + sin4t),y = 775'"'; arcsin9 (x +y) = x3 + /.

·3. y

1

=11(4x+Jcos5x);'y

2

=(x5

+7x)/(J+'-"1+9x).

4.

)'.= 2-•- 2-h ,x0

= 2.

5.

y,

=cos ln 2 x; y2 = JJ;;i 1(1 + .../x). 6.

I/(0, 98)7 ; cos88 .

I. y1 = ctg6 .Jh- '-"arcsin 7x; y2 = tg(l I tfx) ·lg8 (7 x 1 + 5);

v3 =~cos(3x +7.../x); y4

=(arcsm6x)

'Ys-

lglnx·cos

8x

~

xs·sin96x .

4

•

1/cosSx •

39

'·

•

~sin J4x8 + 6x

2.

x =cos6t lsin5t,y = tg(J/(J-7t)); x5 siny = ctgx + i.

3.· y, = ..Jx ·S"'c.,n4x; y2 = tg ln(2 + 3x6)..

4.

y = 4ctgx- cosx Isin 2 x,.x0 = Tr /2. 5. y1 = ..Jx /(1 +In x); y2 = x4 sin 5x,

I

1

sin 1x

1

6

,--;::-

) arctg(2 + X 5 )

. y, =tg--+

3

; y2 =ctg x

4

1

=

J

;

·vm5x; y 3

+ 5x

cos 5x

arcsin 4x4

../i.OU

tgx

s

. 7

6x

~

y

4 =(lnx)

11

·sin

; y

= tg

2

.cos.; Ys =

cos.7x-)4x+~

6

(v3x+ 1lln9x)

7. y~ =1- cos 4x +cos 2x,[O;a /2]; y2 = x 3 + 3x2 -

2,[-2;2].

8; l.JHCJlO 8 pa36HTh Ha .D.Ba CJlaraeMbiX TaK, lfTOObl cyMMa HX

Ky6oB 6bJJia HaHMeHbUJeH.

BapuanT 23.

..rx . 3

x

4

.

~

91tg(x+sin

6

x)

·

1. y =5x+sm

·y =arcsm(1/x)

3 tg5x-y

="

·

I

'

2

'

J

4Xs + 3arcctg9x

'

Y4 = (ctgxyts..!x; Ys = X

49 • ~tg8 5x ln 4 sin 2x. 2arcsi" 42 x;

l.

Y = 8&+ ln 5 9x; y

2

= ctg(1ltfx)· tg6x\ y = arcsin\Jx+ lnx).

1

·

3

"\/2 + arctgx8

'

lllnx

X

58

COS

76167

;

Y4 =(I n In X)

; Ys =

J

17

6x

. ctg

y6

= t1 cos57 [.J5x + 6 /(x4.sin x10 )]

2.

X= 31 /(t +COS 5t),y = 74"mint;

sin 9 (x + y) = x9 + y 9 •

3.

y1 = x 5 .Jcos 5x ); y 2 = lg(3x + J);";i).

4. y = arctgx, x0 = 1.

5.

y1 =sin In~ x; y 2 = (1 + .h)tJ);";i. 6.

1/(2,98i; arctg0,97.

7.

y

1

= x4 - 2x2

+ 5,[-2;2]; h

= x/2+sin 2 x,[-a/l;a/2].

8.

CyMMa KBa,npaTOB .nsyx noJJO:>KHTeJJbHbiX l{HCeJJ paBHO 300.

no.no6-

I

y·

=

~

+ 17cassx · y

·

5X' y· -

61ctg(x2 -x)

·

= tg(1/ x5 )arcctg15

'I

' I

' 2

·

' 3-

•

'

arccos sm 7x

Y

=(cos-hY; Ys =7../6x+'i ·x7 ·Yarcsi~x·ln 9 (x+~);

4

y6

= Jog7 arctg5

( Fx /(3sin x -1)).

2.

X=e' aFCSint 7 ,y=e'arctgt 7 ; r +2Y =x6 + y 5.

3.

1

1 4

= 25.

y1 = x n( + x>; y2 = -Jx /sin cosx. 4. y = 2-Jx /(2 + -Jx),x0

5.

y1 =x · tg9x; y2 =arcsin In x l(x +In x). 6. II ~26, 7; sin 94 ·.

I

y

= .Jsin 7x + 3cos4x. y

_ lg6

5

9 C-:-3tL

4

tg(arctgx )

;

•

I

'

2 -

X. 'JCigx

; YJ =

7x + .Jin cosx

sinux·'</ctg64x

.

_ _::::.__::~~~=='

Y4 =(x + lnx)\ Ys = lg(5x + -Jx). -J6x7 +

4x

I. Y = cos4 6x -I I -Jarcctg.t; y =~sin

7x. 2,xs.•. Y

= ~ctg(cos4x).

1

2

•J

213

+e

r•

x

Y4 = (8x)1/cosl•; Ys = (x 4 -

xt . ~arcsin 2 X ln 6 sin l6x. 2coslx;

y

6

=sin 15 lg(l +arcsin 2x /sin 3x).

2.

X =:tgt /(t 2 + ctgt),y =arcsin! 7 ; exly + eylx = x2 + l.

3.

yl = J);7 arccos x; Y2 = 5.Jcos9x. 4.

y = ctg2x, Xo = 1! I 4.

I. y

,r:=<l

c:::;:

=sin X

4 cosx8 ; Y

arcsin(6x7 -7x)

1

= 'figx

-I I vctg5x; y

2

=

~

;

3

5x15

+ e arccts:

·'

Jx

s . I

nx·ctg

39

x

Y4

= (In In x)

sm

; Ys

=17 .

;

''-JI - 3x17 • 5cos8x

y

6

= arcsin 56 [x8

/(4arctg7x + 4x9 )]

2.

x =sin ln(t /2)

,

y == 3.js,+,·tx9'.

x +

...:.

2x + y'-

,

y-cos--.

x-:-2y

·J. Y1 =~tg4x;y2

=xl(l+5..r;). 4. y=(x2

-2x+2)/x2 ,x0 =2.

5.

y1 =ctg(tg5x); y2

= ../4x +I /ln(l + 5x).

6. lg998; tg153'.

__.,

y1 =x

s

-5x

4

+5x

3

+1,[-l;2];y2

.

7.

=arcctg[(l/x)/(l+x)],[O;l].

I.

2sin4x

+

II

~7

=

if

COS

4 8

. r '

=

4XIJ/7 +X6 '

;

·Y1=

vcfgtx;y2

X·lgvx;y

3

.Jarcsin 8 7x

I.

y =~cos8x-7

5 ·

6

~· y

=ctg(l/x

6

)arctg

19

6x·

y

511 (x 5

-

6x)

·

'"

= v·g

' .

I

'

2

'

3

•

•

'

arcs mtg s m7X

Y4

=(sin~)\ Ys = 5.J4... 2 ·x9

• Z/arccosx ·lg4 (4x+ J../x);

y6 = arcsin 8 (<{7/(3cos9x -1)).

2.

x =arcsine', y = e'ctg/6 ; ?>·

+ 2x =sin~.

3.

y1 =x111n(I+SxJ; y2

=cos3 sinx4 • 4. y=sinx+cosx,x =1!14.

0

1.

.

l-cos.X

2.

•

I'

tgx

3

.

I'

I

I(

x-

1).

I1m

X 3

1m--

1111

n x n

x-+0

x->!!. tg5 X

x-+1

2

4.

lim (~--Jr-_)5.

limxsinx

6.

lim(ctgx/llnx

7. lim(l-x)"os(•rxll)

.x-+Jr/2 ctgx

2cosx

x-+0

x-+0

x-+1

BapaanT 2.

.

1- x

•

In(sin 6x)

.

•

I. hm

sin(;rxI 2)

2. 1un

In sin x

3. 11111 arcsm 3x ·ctg7x

x-.1 I -

.....o

..~o

1

2

x6.1im(ctgx)""x 7.

lim (cosxY'<x-Jr/

2

4. lim(-x----) 5.1im(sin3x)""

)

x-+1

x -l

In x

~.....o

......o ·.

x-+lf 12

BapuanT 3.

10

2 -

)

x

-x

I.

lim x

-

x+

2. lime .-e

'3.

limxlnctgx

4.

lim{ctgx-l/x2 )

x-+1

X 20 -

4x + 3

x-+0

Sll12X

x-+0 .

x-+0

5.

limx186 x

6.

lim(l+2')11 x 7.1im[ln(l-x)t"·'

x~O

x-+x:

x-.0

BapaanT 4.

.ifi+2x + 1

. .

e•- e-x - 2x

3.

.

( 11x

-I)

4.

. 1/ln(•'-1)

!.lim~

2.

11m

X- sin X

1lffiX

3

1lffiX

x-+-1 'J 2 +X +X

x-+0

X-+"'

x-+0

•

.r_.O+

X-+0+

X-+1

BapuauT 5.

I

.

ln(2+3x)

.

e

3

.

(

- _ )

).

2

x -cos3x

(

.

I

.

1

.

1m

X

2

tg

JrX

1m

1m

3

9

X-+oo

.J3 +2x2

X-+0 e4x - CQS 4 r

1

16

X-+)

4.1im(~-

. !

)5.1im(l-cos5xY 6.

lim [ln(l I x)Y

7. limx1'•in 6 x

x-+o

x

sm

3x

x-+o

.

x-+O+

x-+o

BapaanT6.

I

I.

xctgx~l

2

,.

3

'i;-l3

I'

2

-QOix

4

I' ('I

1

)

. nn

2

.

1m

'I tgx

· .

1m x e

·

.

un

---

x-+0

x

X-+Jri 4 2sin 2 x-J

_, .....,

X-tO

X

J'-1

1

6.

lim(sin 7xt•••Jx 7.

lim (tgx) 2x-"

5. lim(l-x) "x

X-+1-

X-+0

X-+IC/2

BapaauT 7.

e111x _ e•

7x -2'

l.lim-

2.

lim

3.

lim(;r-2arctgx)lnx

x-+o

tgx-x

X-+0 3X -

5X

X-+oo

,

4.

lim(_:_ __I_J5.

lim(tg5xY

6. lim(ctg2x)111"'

7. lim(l-xt<•2-

>

x-+1

x - 1

Jn x

.....o

.....o.

x-+1

1

BapaauT8.

1

I.

4

1.

.

I(

3

x

-J6

2

•

cos3x

31.

x

.

1m2

·

2

1m --

un ctgx n x

+ e )

X-+

X

+ 5x

- 6x -16

X-+1Cl2

cos X

x-+O

4. lim (2x2 t<l-cosx) 5.

lim(ln xY'..r;

6. lim(arcsin x)'11-'

X-lo0+

X-+'Xl

.t-tO

·\~[-2(-,--'.rx--=x=-)

3(1-\rx)]

7

I .

..x8

+x3

+2x+2

2.

.

~x-8 +2

I1111

1lm-------

..... -1

X0

-)

x--+0COS3X+COS4x-2

3. limarcsin(x -J)tg(;rx/;)4. lim(

1.

_ _!_)

5.

lim(tg3x).rx

x--+1

.t--+0

arCSII1

X

X.

x-->O

6.

lim(sin;rx)'s<n' 21 7.

lim(S'+x)11 '

x41-

~~o

BapnanT 10.

.

x

8

+ x

6'

.

;r- 2arctgx

.

2 11x'

4

1.

(I

r)

-2

I.

Iun

X 10

-

1

2•

1nn

11

-1

3•

11111 x e

.

1111

n x - v x

x-+1

.t-t+X:

e· X

x-+0

X-++;XJ

5.

lim(x+x2)'6.

lim(lnctgx)'g3x 7.

lim(sinx)

11

(.. -xl

.t-t>O

x-40+

x-+ll-

BapuauT 11.

. sin(ex-l -1)

.

lnx

.

I

.

1111

.

1111

1

tgx n x

I

3. 1111

I

In X

1

1

I +21n sin X

.t-->O+

x-->1

x-->O•

4.1im(+-

1

)5.Iim(;r/2-arctgx)

11

'

6.1im(l-cosx)"'sx

x--+O

Sill

X J -COS X

· x-->+"'

x-->O

7.

lim[h1(1/x)]'

x~O+

BapuauT 12.

.

lncos3x

.

3x-x3 ' . .

;/

6

4

. (

5

3 )

.

1111

. 1111-- 3. 11111VXCtg

x

.

1

--5

---

I

2

1m

3

I

1

((-3

.t-->0.

.t-->1

1-X

}-X

x--+OII1COS4X

.t-->3

5.

lim (I- x)sinn

6.

lim(tg5x)11 x'

7. lim(I/4x).rx

x--+1-0

x->0

x-+Q

BapuauT 13.

I.

.

lnsin3x

2.

.

arctg(x-1)

3.

.

hm .

hm

.J

·

hmarctg3xctg4,x .

x-->0

In smSx

x-+1+0

x2 +X- 2

x-->0