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- Question 1 of 7
##### 1. Question

You buy a call with a strike \(K_1\) and some maturity. You sell a second call with a strike \(K_2>K_1\) and the same maturity. What is the payoff of this strategy?CorrectIncorrect - Question 2 of 7
##### 2. Question

This is a text to show that \(x^*\) and for equations in one line

\begin{equation*} \frac{1}{2} \end{equation*}

CorrectIncorrect - Question 3 of 7
##### 3. Question

test1

CorrectIncorrect - Question 4 of 7
##### 4. Question

At first, we sample \(f(x)\) in the \(N\) (\(N\) is odd) equidistant points around \(x^*\):

\[

f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}

\]

where \(h\) is some step. Then we interpolate points \((x_k,f_k)\) by polynomial

\begin{equation} \label{eq:poly}

P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}

\end{equation}

Its coefficients \({a_j}\) are found as a solution of system of linear equations:

\begin{equation} \label{eq:sys}

\left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}

\end{equation}

Here are references to existing equations: (\ref{eq:poly}), (\ref{eq:sys}).

Here is reference to non-existing equation (\ref{eq:unknown}).CorrectIncorrect - Question 5 of 7
##### 5. Question

\begin{align*} \frac{1}{2} \end{align*}

CorrectIncorrect - Question 6 of 7
##### 6. Question

$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$

\begin{equation*}

1 + 2 = 3

\end{equation*}\begin{equation*}

1 = 3 – 2

\end{equation*}\begin{align*}

1 + 2 &= 3\\

1 &= 3 – 2

\end{align*}\begin{align*}

f(x) &= x^2\\

g(x) &= \frac{1}{x}\\

F(x) &= \int^a_b \frac{1}{3}x^3

\end{align*}\begin{matrix}

1 & 0\\

0 & 1

\end{matrix}\begin{align*}

\frac{1}{\sqrt{x}}

\end{align*}\begin{align*}

\frac{1}{\sqrt{x}}

\end{align*}CorrectIncorrect - Question 7 of 7
##### 7. Question

The well known Pythagorean theorem \(x^2 + y^2 = z^2\) was

proved to be invalid for other exponents.

Meaning the next equation has no integer solutions:\[ x^n + y^n = z^n \]

CorrectIncorrect

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