In my exam the question was to determine the existence of this limit(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \lim_{(r,t)\rightarrow(0,0)} \frac{e^{r^2}}{\cos{t}\sin{t}} [/tex]

now i wrote the numerator has no t associated with it so grows or shrinks without bounds, the same applies for the denominator...

so the limit does not exist

is this a good reason

another question was

[tex] \lim_{(x,y)\rightarrow(0,0)} \frac{\sin{xy}}{xy} [/tex]

i substituted xy = u and got [tex] \lim_{u \rightarrow 0} \frac{\sin{u}}{u} = 1 [/tex]

is this the correct method?

Am i right?

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# Homework Help: Does this limit exist lim e^(r^2)/(cos(t)sin(t)) for (r,t)->(0,0)

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