What is the principal value of $cos^{- 1} (- \frac{1}{2})$ ?

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What is $x \to 0 lim \frac{sin ( 3 x ) tan ( 2 x )}{1 - cos x}$ ?
What is $x \to 0 lim \frac{1 - cos ( 4 x )}{x ^{2}}$ ?
Let $f (x) = {a x^{2} + b, 4 x - 1, x \leq 1 x > 1$ . If $f$ is differentiable at $x = 1$ , what is the value of $a + 2 b$ ?
For $f (x) = x^{3} - 3 x$ on $[0, 2]$ , the Mean Value Theorem guarantees a value $c$ in $(0, 2)$ . What is $c$ ?
What is $x \to \infty lim (4 x^{2} + x - 2 x)$ ?
Let $f (x) = \frac{2 x ^{2} - x - 6}{x ^{2} - x - 2}$ . If the graph has vertical asymptotes at $x = p_{1}, \dots, p_{n}$ and a horizontal asymptote $y = H$ , what i…

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