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1/(1-x²) can be split into the partial fractions A/(1+x) + B/(1-x), where A and B are real constants, which when evaluated by multiplying the equation 1/(1-x²) = A/(1+x) + B/(1-x) th...

The answer to the first part is that the matrix does have an inverse. This is found by finding the determinant of the matrix from the formula ad - bc (for some matrix ( a b // c d ) ) to get the ...

The answer to this question will be explained during the interview session

Euler's Formula is: e^ix = cos(x) + isin(x)

This identity comes from the Maclaurin expansion of the exponential function. The resulting maclaurin series is a power series in x with odd te...

It is possible to solve this question using integration by parts. However, we note that sin(x) is an odd function, meaning that sin(-x) = -sin(x). Thus x²sin(x) is also an odd function. This me...