SORU 1

 

» syms x a b c

» y=[x-(1/a)-(1/b)]*[x-(1/b)-(1/c)]*[x-(1/c)-(1/a)]

 

y =

 

(x-1/a-1/b)*(x-1/b-1/c)*(x-1/c-1/a)

 

» simple(y)

 

simplify:

 

(x*a*b-b-a)*(x*b*c-c-b)*(x*c*a-a-c)/a^2/b^2/c^2

 

 

radsimp:

 

(x*a*b-b-a)*(x*b*c-c-b)*(x*c*a-a-c)/a^2/b^2/c^2

 

 

combine(trig):

 

(x^3*a^2*b^2*c^2-2*x^2*a^2*b^2*c-2*x^2*a*b^2*c^2-2*x^2*a^2*b*c^2+3*x*a^2*b*c+3*x*a*b*c^2+x*a^2*b^2+3*x*a*b^2*c+x*b^2*c^2-2*b*c*a-b*c^2-b^2*a-b^2*c+c^2*a^2*x-c*a^2-c^2*a-a^2*b)/a^2/b^2/c^2

 

 

factor:

 

(x*a*b-b-a)*(x*b*c-c-b)*(x*c*a-a-c)/a^2/b^2/c^2

 

 

expand:

 

x^3-2*x^2/c-2*x^2/a-2*x^2/b+3*x/b/c+3*x/b/a+x/c^2+3*x/c/a+1/a^2*x-2/a/b/c-1/a^2/b-1/a/c^2-1/a^2/c+1/b^2*x-1/b^2/c-1/b^2/a-1/b/c^2

 

 

convert(exp):

 

(x-1/a-1/b)*(x-1/b-1/c)*(x-1/c-1/a)

 

 

convert(sincos):

 

(x-1/a-1/b)*(x-1/b-1/c)*(x-1/c-1/a)

 

 

convert(tan):

 

(x-1/a-1/b)*(x-1/b-1/c)*(x-1/c-1/a)

 

 

collect(x):

 

x^3+(-2/a-2/b-2/c)*x^2+((-1/a-1/b)*(-1/b-1/c)+(-1/a-2/b-1/c)*(-1/c-1/a))*x+(-1/a-1/b)*(-1/b-1/c)*(-1/c-1/a)

 

 

ans =

 

(x-1/a-1/b)*(x-1/b-1/c)*(x-1/c-1/a)

 

» pretty(y)

 

                (x - 1/a - 1/b) (x - 1/b - 1/c) (x - 1/c - 1/a)

»

 

SORU 2

 

» syms x

» f=(x^4)+[4*(x^3)]-[17*(x^2)]+(27*x)-19

 

f =

 

x^4+4*x^3-17*x^2+27*x-19

 

» g=(x^2)+(12*x)-13

 

g =

 

x^2+12*x-13

 

» a=f*g

 

a =

 

(x^4+4*x^3-17*x^2+27*x-19)*(x^2+12*x-13)

 

» simple(a)

 

simplify:

 

(x^4+4*x^3-17*x^2+27*x-19)*(x^2+12*x-13)

 

 

radsimp:

 

(x^4+4*x^3-17*x^2+27*x-19)*(x^2+12*x-13)

 

 

combine(trig):

 

x^6+16*x^5+18*x^4-229*x^3+526*x^2-579*x+247

 

 

factor:

 

(x^4+4*x^3-17*x^2+27*x-19)*(x+13)*(x-1)

 

 

expand:

 

x^6+16*x^5+18*x^4-229*x^3+526*x^2-579*x+247

 

 

convert(exp):

 

(x^4+4*x^3-17*x^2+27*x-19)*(x^2+12*x-13)

 

 

convert(sincos):

 

(x^4+4*x^3-17*x^2+27*x-19)*(x^2+12*x-13)

 

 

convert(tan):

 

(x^4+4*x^3-17*x^2+27*x-19)*(x^2+12*x-13)

 

 

collect(x):

 

x^6+16*x^5+18*x^4-229*x^3+526*x^2-579*x+247

 

 

ans =

 

(x^4+4*x^3-17*x^2+27*x-19)*(x+13)*(x-1)

» pretty(a)

 

                 4      3       2                2

               (x  + 4 x  - 17 x  + 27 x - 19) (x  + 12 x - 13)

»

 

SORU 3

 

» syms x

» expand(tan(4*x))

 

ans =

 

(4*tan(x)-4*tan(x)^3)/(1-6*tan(x)^2+tan(x)^4)

 

» syms x y

» expand(cos(x+y))

 

ans =

 

cos(x)*cos(y)-sin(x)*sin(y)

 

» expand(cos(3*x))

 

ans =

 

4*cos(x)^3-3*cos(x)

 

» expand(cos(6*x))

 

ans =

 

32*cos(x)^6-48*cos(x)^4+18*cos(x)^2-1

 

»

 

 

 

SORU 4

 

» syms x y z

» expand(cos(x+y+z))

 

ans =

 

cos(x)*cos(y)*cos(z)-cos(x)*sin(y)*sin(z)-sin(x)*sin(y)*cos(z)-sin(x)*cos(y)*sin(z)

 

»

 

SORU 5

 

» taylor(asin(x),8)

 

ans =

 

x+1/6*x^3+3/40*x^5+5/112*x^7

 

» taylor(acos(x),8)

 

ans =

 

1/2*pi-x-1/6*x^3-3/40*x^5-5/112*x^7

 

» taylor(atan(x),8)

 

ans =

 

x-1/3*x^3+1/5*x^5-1/7*x^7

 

»

 

SORU 6

 

» syms x y

» y=log(cos(x))

 

y =

 

log(cos(x))

 

» expand(y)

 

ans =

 

log(cos(x))

 

» taylor(expand(y),13)

 

ans =

 

-1/2*x^2-1/12*x^4-1/45*x^6-17/2520*x^8-31/14175*x^10-691/935550*x^12

 

SORU 7

 

» syms y x

» y=[(x+3)/(x*(x+2)*(x+1))]*[(1/3)^x]

 

y =

 

(x+3)/x/(x+2)/(x+1)*(1/3)^x

 

» symsum(y,1,inf)

 

ans =

 

1/4» syms x y n

» symsum(y,1,n)

 

ans =

 

1/2*(n+1)^2-1/2*n-1/2

 

SORU 8

 

» syms x y

» y=x^10

 

y =

 

x^10

 

» symsum(y,1,100)

 

ans =

 

959924142434241924250

 

SORU 9

 

» syms x y

» y=x^(-4)

 

y =

 

1/x^4

 

» symsum(y,1,inf)

 

ans =

 

1/90*pi^4