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lim((g(x)*sin(2x)+e^(2*x)-1)/x),x->0,lim g(x)=5,x->0

 Sep 27, 2015
 #1
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lim((g(x)*sin(2x)+e^(2*x)-1)/x),x->0,lim g(x)=5,x->0

 

So we have

 

lim[(5*sin(2x) + e^(2x) - 1) /x] , x ⇒ 0      using L'Hospital's Rule we have

 

lim [(10cos(2x)  + 2e^(2x)] / 1. x⇒ 0   =

 

10*cos(0) + 2e^(0)   =  10 + 2 =  12

 

 

cool cool cool

 Sep 27, 2015
 #2
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I have not yet learned L'Hospitals rule.Is there another method for this?

 Sep 27, 2015

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