Calcule o termo
no desenvolvimento de ![\left{\left(\frac{a}{x}+\sqrt[2]{x} \right)}^{12}](/latexrender/pictures/1ebc74d7c40a039dd815f7812d01daae.png "\left{\left(\frac{a}{x}+\sqrt[2]{x} \right)}^{12}")
, muito obrigado !Eu aprendi assim:
Numero de termos : 12 - p = 5 (cinco do potencia do x)
7 = p
Então seria :
x 
Sergio
por sergiomorales » Qui Jun 02, 2011 12:28
no desenvolvimento de , muito obrigado ! x 
por carlosalesouza » Sáb Jun 04, 2011 02:34
teremos:
![C_t \cdot a \cdot x^{\frac{t-1}{2}-[(n+1)-t]}](/latexrender/pictures/5d3f89a177ace73b162b7378924d2a09.png "C_t \cdot a \cdot x^{\frac{t-1}{2}-[(n+1)-t]}")
![\\
\frac{t-1}{2}-[(n+1)-t] = 5\\
\frac{t-1}{2}-[(12+1)-t] = 5\\
\frac{t-1}{2}-[13-t]=5\\
\frac{t-1}{2}-13+t=5\\
\frac{t}{2}+t-13-\frac{1}{2}=5\\
\frac{t+2t}{2}=5+13+\frac{1}{2}\\
\frac{3t}{2}=\frac{10+26+1}{2}\\
3t = 37\\
t = 37/3](/latexrender/pictures/b73f0b25e91a429209e0318fb4b950be.png "\\
\frac{t-1}{2}-[(n+1)-t] = 5\\
\frac{t-1}{2}-[(12+1)-t] = 5\\
\frac{t-1}{2}-[13-t]=5\\
\frac{t-1}{2}-13+t=5\\
\frac{t}{2}+t-13-\frac{1}{2}=5\\
\frac{t+2t}{2}=5+13+\frac{1}{2}\\
\frac{3t}{2}=\frac{10+26+1}{2}\\
3t = 37\\
t = 37/3")
![\\
1\left[ \left (\frac{a}{x}\right )^{12}(\sqrt x)^0\right ] +
12\left[\left(\frac{a}{x} \right )^{11} (\sqrt x)^1 \right ] +
66 \left[\left(\frac{a}{x} \right )^{10} (\sqrt x)^2 \right ] +
220 \left[\left(\frac{a}{x} \right )^{9} (\sqrt x)^3 \right ] +
495 \left[\left(\frac{a}{x} \right )^{8} (\sqrt x)^4 \right ] +
792 \left[\left(\frac{a}{x} \right )^{7} (\sqrt x)^5 \right ] +
792 \left[\left(\frac{a}{x} \right )^{6} (\sqrt x)^6 \right ] +
792 \left[\left(\frac{a}{x} \right )^{5} (\sqrt x)^7 \right ] +
495 \left[\left(\frac{a}{x} \right )^{4} (\sqrt x)^8 \right ] +
220 \left[\left(\frac{a}{x} \right )^{3} (\sqrt x)^9 \right ] +
66 \left[\left(\frac{a}{x} \right )^{2} (\sqrt x)^{10} \right ] +
12 \left[\left(\frac{a}{x} \right )^{1} (\sqrt x)^{11} \right ] +
1 \left[\left(\frac{a}{x} \right )^{0} (\sqrt x)^{12} \right ]](/latexrender/pictures/6869473ae78dd41f40f3582da1a09e88.png "\\
1\left[ \left (\frac{a}{x}\right )^{12}(\sqrt x)^0\right ] +
12\left[\left(\frac{a}{x} \right )^{11} (\sqrt x)^1 \right ] +
66 \left[\left(\frac{a}{x} \right )^{10} (\sqrt x)^2 \right ] +
220 \left[\left(\frac{a}{x} \right )^{9} (\sqrt x)^3 \right ] +
495 \left[\left(\frac{a}{x} \right )^{8} (\sqrt x)^4 \right ] +
792 \left[\left(\frac{a}{x} \right )^{7} (\sqrt x)^5 \right ] +
792 \left[\left(\frac{a}{x} \right )^{6} (\sqrt x)^6 \right ] +
792 \left[\left(\frac{a}{x} \right )^{5} (\sqrt x)^7 \right ] +
495 \left[\left(\frac{a}{x} \right )^{4} (\sqrt x)^8 \right ] +
220 \left[\left(\frac{a}{x} \right )^{3} (\sqrt x)^9 \right ] +
66 \left[\left(\frac{a}{x} \right )^{2} (\sqrt x)^{10} \right ] +
12 \left[\left(\frac{a}{x} \right )^{1} (\sqrt x)^{11} \right ] +
1 \left[\left(\frac{a}{x} \right )^{0} (\sqrt x)^{12} \right ]")
![\\
1\left[\frac{a^{12}\sqrt x ^{0}}{x^{12}} \right ] +
12\left[\frac{a^{11}\sqrt x ^{1}}{x^{11}} \right ] +
66\left[\frac{a^{10}\sqrt x ^{2}}{x^{10}} \right ] +
220\left[\frac{a^{9}\sqrt x ^{3}}{x^{9}} \right ] +
495\left[\frac{a^{8}\sqrt x ^{4}}{x^{8}} \right ] +
792\left[\frac{a^{7}\sqrt x ^{5}}{x^{7}} \right ] +
792\left[\frac{a^{6}\sqrt x ^{6}}{x^{6}} \right ] +
792\left[\frac{a^{5}\sqrt x ^{7}}{x^{5}} \right ] +
495\left[\frac{a^{4}\sqrt x ^{8}}{x^{4}} \right ] +
220\left[\frac{a^{3}\sqrt x ^{9}}{x^{3}} \right ] +
66\left[\frac{a^{2}\sqrt x ^{10}}{x^{2}} \right ] +
12\left[\frac{a^{1}\sqrt x ^{11}}{x^{1}} \right ] +
1\left[\frac{a^{0}\sqrt x ^{12}}{x^{0}} \right ]](/latexrender/pictures/510bba62d9ecff8acca314885a6762dd.png "\\
1\left[\frac{a^{12}\sqrt x ^{0}}{x^{12}} \right ] +
12\left[\frac{a^{11}\sqrt x ^{1}}{x^{11}} \right ] +
66\left[\frac{a^{10}\sqrt x ^{2}}{x^{10}} \right ] +
220\left[\frac{a^{9}\sqrt x ^{3}}{x^{9}} \right ] +
495\left[\frac{a^{8}\sqrt x ^{4}}{x^{8}} \right ] +
792\left[\frac{a^{7}\sqrt x ^{5}}{x^{7}} \right ] +
792\left[\frac{a^{6}\sqrt x ^{6}}{x^{6}} \right ] +
792\left[\frac{a^{5}\sqrt x ^{7}}{x^{5}} \right ] +
495\left[\frac{a^{4}\sqrt x ^{8}}{x^{4}} \right ] +
220\left[\frac{a^{3}\sqrt x ^{9}}{x^{3}} \right ] +
66\left[\frac{a^{2}\sqrt x ^{10}}{x^{2}} \right ] +
12\left[\frac{a^{1}\sqrt x ^{11}}{x^{1}} \right ] +
1\left[\frac{a^{0}\sqrt x ^{12}}{x^{0}} \right ]")
![\\
1\left[\frac{a^{12}}{x^{12}} \right ] +
12\left[\frac{a^{11}\sqrt x }{x^{11}} \right ] +
66\left[\frac{a^{10}x}{x^{10}} \right ] +
220\left[\frac{a^{9}x\sqrt x}{x^{9}} \right ] +
495\left[\frac{a^{8}x ^{2}}{x^{8}} \right ] +
792\left[\frac{a^{7}x^2\sqrt x}{x^{7}} \right ] +
792\left[\frac{a^{6}x ^{3}}{x^{6}} \right ] +
792\left[\frac{a^{5}x ^{3}\sqrt x}{x^{5}} \right ] +
495\left[\frac{a^{4}x ^{4}}{x^{4}} \right ] +
220\left[\frac{a^{3}x ^{4}\sqrt x}{x^{3}} \right ] +
66\left[\frac{a^{2}x ^{5}}{x^{2}} \right ] +
12\left[\frac{ax ^{5}\sqrt x}{x^{1}} \right ] +
1\left[x ^{6}]](/latexrender/pictures/00481cca490c4695528e654e7a4c34dd.png "\\
1\left[\frac{a^{12}}{x^{12}} \right ] +
12\left[\frac{a^{11}\sqrt x }{x^{11}} \right ] +
66\left[\frac{a^{10}x}{x^{10}} \right ] +
220\left[\frac{a^{9}x\sqrt x}{x^{9}} \right ] +
495\left[\frac{a^{8}x ^{2}}{x^{8}} \right ] +
792\left[\frac{a^{7}x^2\sqrt x}{x^{7}} \right ] +
792\left[\frac{a^{6}x ^{3}}{x^{6}} \right ] +
792\left[\frac{a^{5}x ^{3}\sqrt x}{x^{5}} \right ] +
495\left[\frac{a^{4}x ^{4}}{x^{4}} \right ] +
220\left[\frac{a^{3}x ^{4}\sqrt x}{x^{3}} \right ] +
66\left[\frac{a^{2}x ^{5}}{x^{2}} \right ] +
12\left[\frac{ax ^{5}\sqrt x}{x^{1}} \right ] +
1\left[x ^{6}]")
![\\
1\left[\frac{a^{12}}{x^{12}} \right ] +
12\left[\frac{a^{11}\sqrt x }{x^{11}} \right ] +
66\left[\frac{a^{10}}{x^{9}} \right ] +
220\left[\frac{a^{9}\sqrt x}{x^{8}} \right ] +
495\left[\frac{a^{8}}{x^{6}} \right ] +
792\left[\frac{a^{7}\sqrt x}{x^{5}} \right ] +
792\left[\frac{a^{6}}{x^{3}} \right ] +
792\left[\frac{a^{5}\sqrt x}{x^{2}} \right ] +
495\left[a^{4}\right ] +
220\left[a^{3}x\right ] +
66\left[a^{2}x ^{3}\right ] +
12\left[ax ^{4}\sqrt x \right ] +
1\left[x ^{6}]](/latexrender/pictures/822589d1bc387024c0d2716308a04aef.png "\\
1\left[\frac{a^{12}}{x^{12}} \right ] +
12\left[\frac{a^{11}\sqrt x }{x^{11}} \right ] +
66\left[\frac{a^{10}}{x^{9}} \right ] +
220\left[\frac{a^{9}\sqrt x}{x^{8}} \right ] +
495\left[\frac{a^{8}}{x^{6}} \right ] +
792\left[\frac{a^{7}\sqrt x}{x^{5}} \right ] +
792\left[\frac{a^{6}}{x^{3}} \right ] +
792\left[\frac{a^{5}\sqrt x}{x^{2}} \right ] +
495\left[a^{4}\right ] +
220\left[a^{3}x\right ] +
66\left[a^{2}x ^{3}\right ] +
12\left[ax ^{4}\sqrt x \right ] +
1\left[x ^{6}]")
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em um sistema de coordenadas cartesianas xOy. Determine o número complexo b , de módulo igual a 1 , cujo afixo M pertence ao quarto quadrante e é tal que o ângulo LÔM é reto.
o ângulo entre o eixo horizontal e o afixo 
. O triângulo é retângulo com catetos 
e 
, tal que 
. Seja 
o ângulo complementar. Então 
. Como 
, o ângulo que o afixo 
formará com a horizontal será , mas negativo pois tem de ser no quarto quadrante. Se 
, então 
. Como módulo é um: 
.
.