Calculus

Limits of Functions

Limits of Functions: Level 1 Challenges

         

x0.10.010.0010.00010.00001x00000 \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 xx approaches 0, then x\lfloor x \rfloor approaches 0 as well?
That is, is limx0x=0 \displaystyle \lim_{x\to0} \lfloor x\rfloor = 0 correct?

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

limx0xx!=? \Large \lim_{x\to0} \dfrac{x}{x!} = \, ?

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

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

Find limx3 \displaystyle\lim_{x\rightarrow 3} x29x3 \dfrac{x^2-9}{x-3}

limx1x1x1=?\large \lim_{x \to 1} \dfrac{|x-1|}{x-1} = \, ?

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