Quantitative Finance
Calculus
Find the value of
\[ \lim_{x \to \infty} \frac{2x + \sin x}{x + \cos x}. \]
Suppose a polynomial function \(f(x) \) satisfies \[ \lim_{x \to 1} \frac{f(x)+2}{x-1} = 3.\] Find the value of \[ \lim_{x \to -1} \frac{[f(-x)]^2 - 4}{x^2 -1}. \]
Evaluate \(\displaystyle \lim_{x \to -\infty} \frac{\sqrt{36 x^2 + 26}}{13 - \frac{x}{12}}\).
Consider the function \[f(x) = \displaystyle \frac{ax^3+bx^2+10x-20}{x^2-1}.\] If \(\displaystyle \lim_{x \to \infty}f(x)=10,\) what is the value of \(\displaystyle \lim_{x \to 1}f(x)?\)
For the function \[ f(x) = \frac{ |x(x+2)| }{ x(x+1) }, \] find the value of \[ \lim_{x \to -2^+} f(x) + \lim_{x \to 0^+} f(x). \]