Let -1 x -x-a1-2 x -x2-b1x-b2-x1-2-x2-3-x3-5 - -1 1 1 - 1x1 - 1x2 - 1x3 - 2x1 - 2x2 - 2x3find -

ϕ _ 1 ( x ) = x+a_ 1 , ϕ _ 2 ( x ) = x^ 2 +b_ 1 x+b_ 2 , x_ 1 =2, x_ 2 =3, x_ 3 =5 Δ = 1 amp; 1 amp; 1 ϕ _ 1 (x_ 1 ) ...

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Continuity of a Function

Let ϕ1 x =x...

Question

Let $ϕ_{1} (x) = x + a_{1}, ϕ_{2} (x) = x^{2} + b_{1} x + b_{2}, x_{1} = 2, x_{2} = 3, x_{3} = 5$
$Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 ϕ_{1} (x_{1}) & ϕ_{1} (x_{2}) & ϕ_{1} (x_{3}) ϕ_{2} (x_{1}) & ϕ_{2} (x_{2}) & ϕ_{2} (x_{3}) \end{matrix} ∣ ∣ ∣ ∣ ∣$
find $Δ$

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Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} a_{1} + b_{1} x^{2} & a_{1} x^{2} + b_{1} & c_{1} a_{2} + b_{2} x^{2} & a_{2} x^{2} + b_{2} & c_{2} a_{3} + b_{3} x^{2} & a_{3} x^{2} + b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

x_{i}, y_{i}, z_{i} \in R (i = 1, 2, 3), x \in R

x

Δ = 0

x = 1, - 1

∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣ = 0

Δ = 0

Δ (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} (x - 2) & (x - 1)^{2} & x^{3} (x - 1) & x^{2} & (x + 1)^{3} x & (x + 1)^{2} & (x + 2)^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣

Δ

- k

\frac{(\sqrt{x})^{\frac{3}{5}} \times (\sqrt{x})^{\frac{2}{5}} + 2 \sqrt{x}}{2 ((\sqrt{x})^{\frac{2}{3}} \times (\sqrt{x})^{\frac{1}{3}}) + \sqrt{x}}

\frac{1}{1 - 2 x + x^{2}} = 1 + b_{1^{X}} + b_{2} x^{2} + b_{3} x^{3} + \dots \infty

b_{1}

(1 + x) (1 + x + x^{2}) (1 + x + x^{2} + x^{3}) \dots + (1 + x + x^{2} + . . x^{n - 1}) = a_{o} + a_{1} x + a_{2} x^{2} + . . a_{m} m x^{m}

a_{0} + a_{1} + a_{2} + \dots \dots \dots + a_{m} =

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