) Expand[poly] - poly.
In[1]:= t = (2 + 4 x^2)^2 (x - 1)^3;
In[2]:= Expand[t]
Out[2]= 4 + 12x - 28 + 52 - 64 + - +
b) Factor[poly] - . .
In[3]:= Factor [%], % - (Out[2])
Out[3] = 4
c) Collect[poly] - .
Collect[poly, x] - , x.
In[4]:= u = (1 + 2 x + y)^3;
In[5]:= Collect[u,x]
Out[5]=
d) Simplify[expr] - expr.
In[6]:= Simplify[%]
Out[6]=
) PolynomialQ[expr, x] - True, expr x.
b) Variables[poly] - .
In[7]:= Variables[u]
Out[7]= {x, y}
c) Length[poly] - , .
In[8]:= Length[u]
Out[8]= 2
d) Exponent[poly, x] - y.
In[9]:= Exponent[u, y]
Out[9]= 3
a) Numerator[expr] - expr.
b) Denumenator[expr] - expr.
c) Expand[expr] - , .
In[1]:= V=(x - 1)^2 (2 + x) / ((1 + x) (x - 3)^2);
In[2]:= Expand[V]
Out[2]= - +
d) ExpandAll[expr] - Expand , .
In[3]:= ExpandAll[V]
Out[3]= - +
e) Together[expr] - .
In[4]:= Together[%]
Out[4]=
f) Apart[expr] - .
In[5]:= Apart [%]
Out[5]=
g) Factor[expr] - .
In[6]:= Factor[%]
Out[6]=
h) Simplify[expr] - ,
In[7]:= Simplify[%%]
Out[7]=
a) :
D[f,u] - f u;
In[1]:= D[Sin[x^2]*x, x]
Out[1]:= 2 x2 Cos[ x2 ] + Sin[ x2 ]
In[2]:= D[ x^2 * y^2, y, x]
Out[2]:= 4 x y
D[f,{x, n}] - f x n- .
In[3]:= D[Sin[ x ]*x^2, {x, 2}]
Out[4]:= 4 x Cos[ x ] + 2 Sin[ x ] - x2 Sin[ x2 ]
b) :
Integrate[f,x] - ;
In[1]:= Integrate[ x * Sin[ x ], x]
Out[1]:= -x Cos[ x ] + Sin[ x ]
Integrate - ;
In[1]:= Integrate[ x * Sin[ x ], {x, -10, 10)]
|
|
Out[1]:= -20 Cos[ 10 ] + 2 Sin[ 10 ]
Integrate - .
In[1]:= Integrate[ x^2 + y^2, {x, 0, 1}, {y, 0, 1}]
Out[1]:= 1/3
c) , :
Sum - i;
In[1]:= Sum[ x^n/(n!), {n, 1, 5}]
Out[1]:= x + x^2/2 + x^3/6 + x^4/24 + x^5/120
Series - ;
In[1]:= Series[ f[x], {x, 0, 3}]
Out[1]:=
Limit - .
.
Mathematica . < == >.
a) :
lhs == rhs, rhs - , lhs - .
a) :
,
:
a x^2+b x+c == 0
{ a x^2+b x+c == 0, a x+b == 0} 2-