Tutor profile: Frank B.

Find the domain of the function: $$ \frac{x^2 + 3x + 1}{x - 4}$$. Express using interval notation.

Rational functions have a domain of the entire real number set except for those values that make the denominator equal to zero. Solving for $$x - 4 = 0$$, we get $$x = 4$$. Thus the domain of the function is $$(- \infty, 4) \cup (4, \infty)$$.

Find the derivative of $$x^3 + 3x^2 - 6x + 10.$$

Using the power rule for derivatives, the derivative is: $$ 3x^2 + 6x - 6.$$

When would it be appropriate to use the Normal distribution as an approximation to the t-distribution?

Because the t-distribution converges to the Normal distribution with a high enough degrees of freedom, it's appropriate to use the Normal distribution approximation when the sample size is greater than 30.