If $A$ is a $2 \times 2$ matrix with $det A = 5$ , what is $det (2 A)$ ?

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In the binomial expansion of $(x + \frac{1}{x})^{10}$ , what is the term independent of $x$ ?
For $y = ln (\frac{1}{c o s x} + tan x)$ , determine the first derivative $\frac{d y}{d x}$ with respect to $x$ for all $x$ in…
If $z = 1 + i 3$ , what is the polar trigonometric form of $z$ ?
What is the limit $lim_{x \to 0} \frac{e ^{3 x} - 1}{2 x}$ ?
If a continuous curve has inflection point at $x = c$ , which statement must be true regarding $f^{''} (c)$ if it exists?
Find the slope of the tangent to the curve $x^{2} + y^{2} - 4 x + 6 y = 0$ at the origin $(0, 0)$ .