Quantitative Finance

# Limits of functions - Problem solving

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 $\lim_{x \to -2^+} f(x) + \lim_{x \to 0^+} f(x).$

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