Calculus

# Limits of Functions: Level 1 Challenges

$\boxed{\begin{array}{c|r:r:r:r:r} x & 0.1 & 0.01& 0.001& 0.0001& 0.00001\\ \hline \lfloor x \rfloor & 0 & 0 & 0 & 0 & 0 \end{array}}$

By looking at the table above, is it true that as $$x$$ approaches 0, then $$\lfloor x \rfloor$$ approaches 0 as well?
That is, is $$\displaystyle \lim_{x\to0} \lfloor x\rfloor = 0$$ correct?

 Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

$\Large \lim_{x\to0} \dfrac{x}{x!} = \, ?$

Note: Treat $$x! = \Gamma(x+1)$$.

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

Find $$\displaystyle\lim_{x\rightarrow 3}$$ $$\dfrac{x^2-9}{x-3}$$

$\large \lim_{x \to 1} \dfrac{|x-1|}{x-1} = \, ?$

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