University:
California State University, Northridge
Course:
MATH 150B | Calculus II
Academic year:

2023
Views:

241

Pages:

14
Author:

anon

AFF18. cas f(x) = 1 at x=0. Find / /f(x)=(2+2)x+2f(x) c-l(x+2)(x+2)f"(x) 2(x)2)3,flo) = 1/2p'(0)4Tk!f (o) =k=o4T2,0(x) 4/2 (x)22!T2,0(0.1) = 3818800(b) f(x) = 5x at x = 25. Find 28fex) f(25) 5f(2) 10f"(x) = 1/2 f"(25) = 500= 5/1 + to (2-25)50(x-25)22!= - (x-25)25.2-2-251000T2 25(28)=5+ 28-25 (28-25)101000= 5+3 10 - 91000 at a. . Find tan'(2)f(x) = tan' (x) flowflas.f((1) = 1/1/2T2,1())= o! M (x-1)' - 12-13-2+ 2 4 4 I + 1/2 1/4 =19.ca)wEk=olim(h+1):(x-2)**)3h+1=(n+1)!3th(x-2)**n!(x-2)At 3(x-2)"3n= 3 = faxes 0 x = 2R.O.I.f2}(6)k+3(-1)"(leading terms)lim(-1)"(x+1)" /n+4 (-1)" (-1)" 2++1 (x+1)" (x+1) 941 | n SEE = /(***) for 4/6 = 1x+11 ( )R=1 "Ex" 00k=o9k(n+1).x2n+2Cleading terms)him9n+12n+2n+1ms8=x9n=nxit9"++1x xn1x4n.x on=or99an1x1<91x1<3R=319.ca)' W & (x-2)kkey 3" V k(x-2)(leading terms)lim3nd'/n+1(x-2)8°S==1x-2/-It=(x-2)"(x-2)"31x-21 - 11/++13In33'5-3< x - 2 ( 3When x - l;-1 x x 5 5DOIN(-3)kkel3th(-1)k. 3* 3k EC-1) bn 1/1,fex) 1/1kel Vkf(x)=i) lim n-100 1:0021/4<0forx x 1xii) bn if decreasing cuz f'(x) 50⑇ Converges by A.S.TWhen x = 5;iN (3)88=Wkelthekal1/4-Wkayk 1/2Diverges by P-series TestI = [-1,5) lim (n+1)"(x-1)" n (2-1)" (21) 1x-11 = 1x-1/21-1 cos(5x) = (d) flow.=e**-1=1/2xxxx(x2-x65!1 120(f) fex). = ln(14x) =21.000 fw = as (x-1)h (x-1)h =2XL/11-(x-1)1x-11<2I===2-x+1 3-x 3-x2 2-111.x > 0x>o toFind: x2-2x<3 22.(a)f(o) = If(x) - In 2.2f(10)==ln2=f"(xx) - In2.ln2.ln2.2 xf"(0) : - (ln2)3= ln2(x)' (ln2)'(x) (ln2)'x32:31=1-(ln 2)x (m2)2, (ln2)x'26.00(b) f(x) x thf(4).32P(4)P(4)T(x) = o! offex) = sin(2x)f(x) - 200(2x)f"(x) =-8cos(2x)f"(x) 16 sin(2x)f'(x) = 32cus(2x) f(i) =f"(x) = (64 3in(7) - 64T(x) = 1+ - 4(1) 31 16(x-4)4 56! 23. ca s' sin x dx = = p2 1 - dx= 2-00 - (1- 1/2 = 12-19-19 2 -= 36-8-18+111=1818(b) ' ws (x4) dx = dx = x-= + = 1-1+1- 18 is = 2- 2/2/20 18 36-2 18 = 34 18 9 = 17 24) casfootedt-y-1x ( y y) - 1et x-3-set z-3yx-3(x-3)23int. 3ly.3cost+2 cost =(x)'+x'+(y-2)-9(d) "formsy - sin't = 1- - cos'ty = 1-x2 25) (a) Sxidt=2lyst'm >dy= 3t2 = 3.2 =dx2t2.2When t 2 ; x = 2 . 4y=2j=8 (4,8)Y-8=3(x-4)y = 3x-12+8yz3x-4(b)x = ln t tel{m = dys.1+t'y t an't =dx1/41+t2 1+1tWhen(0, 2)9-1-1(--0)y4y r sin o6yyx'+y' = r2x'+y's2x + 42 = 6y= (Complete the square) (b) r =32 cos o . sin o2r cos (9 9 + r sin 01 =32x + y = 327.(a) r==3 30 , 0 2 030=> x e cos o=> y e 30 sinso30m = dy Be sin O t e .=dx30 -e 30 sin O0=0=3e°1(0) - e sin (0)3When 0.0; x = e : cos (0) = Iy =e°.sin (0) =0 (1.0)9.1(x-1)y= x-133 Tangent Line to poler curveWhenfairedx = cos o 20.cos o(F,F2)=) 2 sin 20 . sin Ody.e[ 2 0.sin20]y -m==dxy =z-x+252imlos = 2004.005.1==-1 =cos 2 cos TZ -E2o Arclength of Poler CurvesadoEg. '' from 0 to 504+ (20)2 do = pt 5 02(02+4) do- prO0'+4dou=o2+4du . 20 doState dudayo= = (27-8)-15 0 00 to 0 . 3dodoP.'20 do= /1.0n'2 [ In 2 ]=/1 th 2 [ ln2 x(a)" r = 2 00(20)r=52r. 2 an 20A=2.1 (VI) do.ANDonly findandAx2from originline paver both cones=p:2 00 (20) = 52COS 20 . II21.20.1- 4A2"0."sin 4 $12.0022si 171/22 (b)"A(1-030) 10 + cos'o dolos O1-coso1-20000 + cos 20 do - 1=1 + cos 2027/3=1/30-2010 - + sin 4 1 o + [0.5m2we o =sin'tcos of 1422534 2 2 2 ]+J3=16=