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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.

Limits of Functions: Level 2 Challenges

$\lim_{x\to\infty} \dfrac{\sin x}x = \, ?$

$\Large \lim_{x\rightarrow 0} \frac{|2x-1|-|2x+1|}{x}= \ ?$

$f(x) = \large{\begin{cases} (x^2 - 4)/(x-2), & \text{ if } x < 2 \\ 2, & \text{ if } x = 2 \\ x^3-3x^2 + 2x + 4 , & \text{ if } x > 2 \\ \end{cases} }$

Compute $$\displaystyle \lim_{x \to 2} f(x)$$.

Given that $$f(x) = \dfrac1{x-1}$$ and $$g(x) = \dfrac3{x^2-3x+2}$$, find $$\displaystyle \lim_{x\to1} \dfrac{f(x)}{g(x)}$$.

$\large \lim_{x \to 0} \, \left \lfloor \dfrac{(\sin x) (\tan x)}{x^2} \right \rfloor = \ ?$

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