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Решение.

Найти значения функции   [tex]\bf w=3t^2+2z^2-v[/tex]   в точках  [tex]\bf P(\, \sqrt2\, ;\, 1;-2\, )[/tex]  ,

  [tex]\bf Q(\, c\, ;\, \sqrt{c}\, ;\, \dfrac{1}{2c}\ )[/tex]   и    [tex]\bf R(\, v\, ;\, 1+\Delta x\, ;\, 2-\Delta x)\ \ .[/tex]  

[tex]\bf w(P)=3\cdot (\sqrt2)^2+2\cdot 1-(-2)=3\cdot 2+2+2=10\\\\w(Q)=3\cdot c^2+2\cdot (\sqrt{c})^2-\dfrac{1}{2c}=3c^2+2c^2-\dfrac{1}{2c}=5c^2-\dfrac{1}{2c}=\dfrac{10c^3-1}{2c}[/tex]  

[tex]\bf w(R)=3\cdot (2-\Delta x)^2+2\cdot (1+\Delta x)^2-(2-\Delta x)=\\\\=3\cdot (4-4\Delta x+(\Delta x)^2\, )+2(1+2\Delta x+(\Delta x)^2)-2+\Delta x=\\\\=12-12\Delta x+3(\Delta x)^2+2+4\Delta x+2(\Delta x)^2-2+\Delta x=\\\\=5(\Delta x)^2-7\Delta x+12[/tex]