(Step-by-Step) (a) Use de l'Hôpital's rule to calculate lim _x \rightarrow 0 frac sin (2 x)-2 xx^3. (b) Does lim _(x, y) \rightarrow(0,0) (sin (2 x)-2
Question: (a) Use de l'Hôpital's rule to calculate \(\lim _{x \rightarrow 0} \frac{\sin (2 x)-2 x}{x^{3}}\).
(b) Does \(\lim _{(x, y) \rightarrow(0,0)} \frac{\sin (2 x)-2 x-y}{x^{3}+y}\) exist?
Deliverable: Word Document 
![[Step-by-Step] Use the definition to calculate the](/images/solutions/MC-solution-library-72394.jpg "[Step-by-Step] Use the definition to calculate the directional")
[Step-by-Step] Use the definition to calculate the directional
(Solution Library) Show that v_1=(c-1 , 1 , 0), v_2=(c-5 , 1 ,
![[Step-by-Step] Let f: R^3 \rightarrow R be](/images/solutions/MC-solution-library-72396.jpg "[Step-by-Step] Let f: R^3 \rightarrow R be differentiable. Making")
[Step-by-Step] Let f: R^3 \rightarrow R be differentiable. Making
![[All Steps] Let F: R^2 \rightarrow R^4](/images/solutions/MC-solution-library-72397.jpg "[All Steps] Let F: R^2 \rightarrow R^4 be the function given by")
[All Steps] Let F: R^2 \rightarrow R^4 be the function given by
(See Solution) Consider the functions f: R^2 \rightarrow R^2 and
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