Menu Close

Question-211895




Question Number 211895 by Spillover last updated on 23/Sep/24
Answered by mehdee7396 last updated on 23/Sep/24
lim_(x→∞)  (1+(a/x)−(4/x^2 )−1)2x  =lim_(x→∞)  (((ax−4)/x^2 ))2x=2a  ⇒lim_(x→∞)  (1+(a/x)−(4/x^2 )−1)^(2x) =e^(2a)   ⇒2a=3⇒a=(3/2) ✓
limx(1+ax4x21)2x=limx(ax4x2)2x=2alimx(1+ax4x21)2x=e2a2a=3a=32
Answered by BHOOPENDRA last updated on 23/Sep/24
we know if we have function  lim_(x→a)  f(x)^(g(x)) =1^∞   then we use the property   lim_(e^x →a)  g(x) {f(x)−1}  So lim_(e^x →∞)  2x (1+(a/x)−(4/x^2 ) −1)=e^3   lim_(e^x →∞)  2x ((a/x)−(4/x^2 ))=e^3     e^(2(a−(4/∞))) =e^3   e^(2a) =e^3   2a=3  a=(3/2)
weknowifwehavefunctionlimxaf(x)g(x)=1thenweusethepropertylimexag(x){f(x)1}Solimex2x(1+ax4x21)=e3limex2x(ax4x2)=e3e2(a4)=e3e2a=e32a=3a=32
Commented by Spillover last updated on 24/Sep/24
thanks
thanks

Leave a Reply

Your email address will not be published. Required fields are marked *