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

2023
Views:

198

Pages:

9
Author:

anon

100 $ due x (log,(x3)(e) do tan (1)(IT/A-1=2x 10g, x3 + l2 2xx3==1 4 1/2x 1) x2+1xx2x logIn 2(f) 105'(5")- ln5.5"(b) Tx of log, x+1=1-52x= Ix log los, (x+1)2.(a) dxf x = d Sxlnx edxdadr ln 3 ln3dln x2 - ln(x+1)=(21/L lnx + F)1 ( X 2x(b) of (sin x)* d exin(sing) een 3dx=ln3 1/3 ( 2/2= [en (sin x) x cos xsin(c) d & (3)- [ n +x cot x" (2x+1) = AllJx= is ((norx-3)=[3ln(2x+1) + 2x+ 6x ](2x+1)"x63" - (xln(3)-3)3.(a) dxu x x ' - 1du = 3x2 dx. 155" du(d) d sec'(x')day. = x 2 dedx11.543 ln 52x=5x3-11.+C3In 52x/x-1 (b) dxu=ln(f)3dx =1-3 =dxdu= dx/1-92I-(3*)2= S ln x dxx ln 2In 3 / 1 - 12u=321/2 Su dudu = In 3.3 dx=1. sin'( 3*)+cln3(lnx)2 +du = 3 dx=ln32 ln 2(c) up dx u=x24(a) lim as+a x xx = lim et lnx = lnxV1-x4du x dx-2eL HOP1-(x)=e.e1=(b)lim(1-1-"lim3xln(1-1)x-s - 00xe11-42x-s+oaln(1-k)sin'tx2)+c 2==eL'HOP1/22sin xextra1-kx3x4=(d)Sdxu=ws-1x-11 + cos' xdu - -sin xdx3x'I-3x-3x=x-1x(1-1')e-31-1/2=e-3tant ( cos x ) + c(e)Sxpdx(c) lim (2+7))* = e e ln(2+7") x818x/9x2-1L'HOP G7.7 = 7.8m7= e limotoo=2+7' *(2,+1)x/(3x):-e h 7sec+ (13x1) + limInfx(d) lim (5x) bnx=ex-o+lnlim1/2 laxx-so+.e x->++bast 2eee5(a)lim2x=2-50008x3aLHOPL'HOP, HepIn2.2lim(l22)'.2((n2)'2 "===8x-> 83x26x6f (x) >> g(x)(b)limln x 38=2500(lnx)28L'HOP3x2lim3==02 lnx2 enxxg (x) >> f (x)6.00 S x2 COS 2x dxu x x 2 dv. = Scos 2x dxdu = 2x dx V= sin 2x2=uv-S V du = x2 sin 2x - S sin 2 2x 2xdxU = x dv = P sin 2x dx2du = dxV = - cos 2x=x2 sin 2x + x COS 2x - s cos 2x dx2222x2 sin 2xx cos 2xsin 2x+-=+224 (6.(b)u=sin'(x) du-fide2 a= x sin'(x) - Special 1-x2 dxa = 1 - x 2du = -2x dxsim'(x) + 1/2 S 1/1 du=x=xu=lnxx'du= dx=- lnx=x(d)u.clnx)du = 2 ln x dxV = x= x(lnx) S 2 lnx dxu = ln xdu dx V = xx(ln x)2- - 2xlnx+2x+c (e) S ex -x cos 3x dx = Su=e"dv = S w s 3x dxdu . . e x dxsin3xV =3=e-x 3in 3xIe-x-x+sin3rddV = fsin 3x dx33dU .-e-dxV=-cos 3x-x-x3esin3x1/m-e-"x=+[cos3x3- 1s 3 e**cos 3x J3-xSex-xsin3xecos3x=--391/4S10Se-x=sin 3xexcos3x-939S = 3e" sin 3xe cos 3xc1010(f) S mix dxu = 5xdu == s sin (w w du2/x dx = 2/1/2 2u dxw du = dx= 2u cos u + S20034 duU= zudv sin u du=-2u cosudu 2 du V cos.u= - 2 5x us Sx = xu=sindxdu = cos = x dxSC1-U2)2S1+04-242du=(b) S in 3 xdx=Ssin xsin'xcos'xdxu = cos xcos'x-du=sin x dx=dxcos2du.(u+c-=+cos xcc) S sin** c os'x dx = I 1 - cos 2x , 2 * 1 + cos 2x dx2= 19, cos22x dx= 1 S sin 2x dx = 1/4 S 1 - 00 4 X dx2= cos 4 x dx=1/2 8 - sin 32 4x + dx = Speck tan x tan'x dxu = see := (sec2'x-1) dxdu - sec x tan x dx=Sub-1 dusec x + c3= ST dxx =2 sin Qdx = 2cos o=x = s s n o2sin 0 = =x,0O = sin ( s)/4-x2= do12==120 + sin 20 + C= O+C2 14-x2+c += 2 9.60 $ x x + dx = = x dx 2 P x 2 + 9dxx - 9xx(x2-9)x(x-3)x+3)== SABc++xx-3x+3+dxxx-3x+3=- ln / x 1 + ln/x-31. ln/x+31 +x 2 9 = A(x-3)(x+3) (x)(x+3)+ C (x)(x-3)When x=0; 9 = -9A A=-1When x 3 ;18 = 18B =B=1When x = 3 ; 18 = 18C=) C = (b) x+3 dx = State x-1 1. dx(x+1)(cx-1)x+1= ln/x-11 +3 ln/x+1/ +1+x+1x+3 = A + B + (c)(x+1)(x-1) x-1 x+1 (x+1)2x + 3 = A(x+1)2 + B(x+1)(x-1) + (x-1)When x 1; 4 =4A =) A=1When x = -1; 2==2 =) C = -1When x = O; 3A-B-C -3 =1-B+1 => B = 1