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x0.10.010.0010.00010.00001⌊x⌋00000 \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}} x⌊x⌋0.100.0100.00100.000100.000010
By looking at the table above, is it true that as xxx approaches 0, then ⌊x⌋\lfloor x \rfloor ⌊x⌋ approaches 0 as well? That is, is limx→0⌊x⌋=0 \displaystyle \lim_{x\to0} \lfloor x\rfloor = 0 x→0lim⌊x⌋=0 correct?
Notation: ⌊⋅⌋ \lfloor \cdot \rfloor ⌊⋅⌋ denotes the floor function.
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limx→0xx!= ? \Large \lim_{x\to0} \dfrac{x}{x!} = \, ? x→0limx!x=?
Note: Treat x!=Γ(x+1) x! = \Gamma(x+1) x!=Γ(x+1).
limx→∞sinxx= ? \lim_{x\to\infty} \dfrac{\sin x}x = \, ? x→∞limxsinx=?
Find limx→3 \displaystyle\lim_{x\rightarrow 3} x→3lim x2−9x−3 \dfrac{x^2-9}{x-3} x−3x2−9
limx→1∣x−1∣x−1= ?\large \lim_{x \to 1} \dfrac{|x-1|}{x-1} = \, ? x→1limx−1∣x−1∣=?
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