×

## Limits of Functions

What happens when a function's output isn't calculable directly – e.g., at infinity – but we still need to understand its behavior? That's where limits come in. See more

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

×