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anonymous
 one year ago
State the value of the limit, if it exists
lim x→0 sin(x) multiplied with 3x^3+2x^2/x^2
Anybody? :)
anonymous
 one year ago
State the value of the limit, if it exists lim x→0 sin(x) multiplied with 3x^3+2x^2/x^2 Anybody? :)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok this is a big one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0first we separate the lim

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 0} (3x+2) \times \lim_{x \rightarrow 0}(\frac{ \sin(x) }{ x ^{2} })\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i forgot to times x^2 with sin(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 0}(\frac{ \sin(x)x ^{2} }{ x ^{2} }) \times \lim_{x \rightarrow 0} (3x+2)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ur following the steps right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03x+2 is a polynomial and thus everywhere continuous so \[\lim_{x \rightarrow 0} (3x+2)= 2+3(0)=2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and the \[\lim_{x \rightarrow 0} \frac{ \sin(0) \times 0 }{ 0 } =0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if u have similar denominator like x^2 in ur case u can separate the limit

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have to go through it a few times to make sure I understand everything :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Any possibilities of some followup questions later on?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0you simply can not say this: \[\lim_{x \rightarrow 0}(\frac{ \sin(x)x ^{2} }{ x ^{2} }) \] \[\implies \lim_{x \rightarrow 0} \frac{ \sin(0) \times 0 }{ 0 } =0\] the whole point of this is that dividing by zero you cannot do, so you check what the function in question does as you approach very close to zero. so: \[\lim\limits_{ x→0} \, \, \sin(x) .\frac{3x^3+2x^2}{x^2}\] \[=\lim\limits_{ x→0} \, \, \sin(x) .\lim\limits_{ x→0}\frac{3x^3+2x^2}{x^2}\] \[=\lim\limits_{ x→0} \, \, \sin(x) .\lim\limits_{ x→0}\frac{\frac{3x^3}{x^2}+\frac{2x^2}{x^2}}{\frac{x^2}{x^2}}\] \[=\lim\limits_{ x→0} \, \, \sin(x) .\lim\limits_{ x→0}\frac{3x+2}{1}\] \[=0 \times 2 = 0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much for your reply! :)
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