Exercise

  1. Express $\cos ^{7}\theta $ in the form
    MATH

  2. Find a function $f$ such that
    MATH

  3. Find all $x$ such that the determinant of the matrix
    MATH
    is zero.

  4. Let
    MATH
    Find the recurrence relation satisfied by $p_{n}.$

  5. Let $f(x)=e^{1/x}$ and let MATH Find the recurrence relation satisfied by $p_{n}.$

  6. Express MATH in the form
    MATH

  7. Draw the graph of MATH over the interval $[-0.04,0.04].$

  8. Find conditions on $a,b,c,d$ so that
    MATH

  9. List the coefficients $a_{k}$ appearing in the formula
    MATH
    for MATH with the spreadsheet.

  10. Find all positive integers $r\le 19$ such that $x^{20}+x^{r}+1$ is divisible by $x^{2}-x+1.$

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