ED 2Semestre (1-31)

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1.28=-4.-7 28=28

20)AB=(x2-x1,y2-y1) A=(-1,0) B=(-2,1) AB=(-2-(-1),1-0) AB=(-1,1)

|AB|=√(-1)²+1² AB/|AB|=(-1/√2,1/√2) |AB|=√1+1 AB/|AB|=(-1.√2/√2.√2,1.√2/√2.√2) |AB|=√2 AB/|AB|=(-√2/2,√2/2) |AB| 21)V(t)=6t³+1,5t V(t)=6.2³+1,5.2 V(t)=6.8+3 V(t)=48+3 V(t)=51

22)V(t)=6.t³+1,5t V’=3.6t²+1,5 V’=18t²+1,5 V’=18.2²+1,5 V’=18.4+1,5 V’=72+1,5 V’=73,5L/min

23)y=(x+16).senx

y’=u’.v+u.v’ y’=1.senx+(x+16).cosx y’=senx+(x+16).cosx 24)f(x)=x³-8 xo=-2 y’=3x² a=f’(-2) f’(-2)=3.(-2)² f’(-2)=3.4 f’(-2)=12

25) f(x)=ex.sen(2x) u=2x f’(x)=(ex.senu+ex.cosu).u’ u=2 f’(x)=((ex.(senu+cosu)).u’ f’(x)=((ex´(sen2x+cos2x)).2 f’(0)=((e0.(sen2.0+cos2.0)).2 f’(0)=((1.(0+1)).2 f’(0)=1.2 f’(0)=2

26)u=(2,-4) u.v=(2.0+4.-3) v=(0,-3) u.v=(0+12) u.v=12

27)u=(2,-4) 2.u=(2.2,2.-4) 2u(4,-8) v=(1,-2) 5.v=(5.1,5.-2) 5v(5,-10) 2u.5v=(4.5+(-8.-10)) 2u.5v=(20+80) 2u.5v=100

28)u=(2,-4,2) A=|u˄v| v=(1,-4,0)

|ij k i j| ijk |u˄v|=|1-40 1 -4| -80-4 |2-42 2 -4| -(0-28) (-8,-2,4)

A=|(-8,-2,4)|=√(-8)²+(-2)²+4²=√84 A=2˄√21

29)|u|=2 A=b.h |v|=3 A=|u|.|v|.senθ/2 θ=30º A=2.3.0,5/2 A=1,5uA

30) u=(1,-2,-1) v=(2,1,0)

w.u=0 (a,b,c).(1,-2,-1)=a-2b-c=0 w.v=0 (a,b,c).(2,1,0)=2a+b =0

a-2b-c=0 w=√2²+(-4)²+10²=2√30 2a+b =0 w=√4+16+100=2√30 a²+b²+c²=2√30 w=√120=2√30

w=2√30=2√30 2a+b=0 a-2b-c=0 2.2-4=0 2-(-2.-4)-10=0 w=(2,-4,10) 0=0 2+8-10=0 |w|=2√30 0=0

31)u=(1,-2,-1) v=(2,1,0)

u.v=(1.2+(-2.1)+(-1.0)) u.v=(2-2+0) u.v=0